Soo tang tan calculus for the managerial, life, and social sciences, (7th edition) cengage learning (2005)

ABOUT THE COVER
Peter Blair Henry received his first lesson in international economics at the age of 8, when his
family moved from the Caribbean island of Jamaica to affluent Wilmette, Illinois. Upon arrival in
the United States, he wondered why people in his new home seemed to have so much more than
people in Jamaica. The elusive answer to the question of why the average standard of living can
be so different from one country to another still drives him today as an Associate Professor of
Economics in the Graduate School of Business at Stanford University.
Henry began his academic career on the campus of the University of North Carolina at Chapel
Hill, where he was a wide receiver on the varsity football team and a Phi Beta Kappa graduate in
economics. With an intrinsic love of learning and a desire to make the world a better place, he
knew that he wanted a career as an economist. He also knew that a firm foundation in mathematics would help him to answer the real-life questions that fueled his passion for economics—
a passion that earned him a Rhodes Scholarship to Oxford University, where he received a B.A.
in mathematics.

PETER BLAIR HENRY
International Economist

This foundation in mathematics prepared Henry for graduate study at the Massachusetts Institute
of Technology (MIT), where he received his Ph.D. in economics. While in graduate school, he served
as a consultant to the Governors of the Bank of Jamaica and the Eastern Caribbean Central Bank (ECCB). His research at the ECCB
helped provide the intellectual foundation for establishing the first stock market in the Eastern Caribbean Currency Area. His current
research and teaching at Stanford are funded by the National Science Foundation’s Early CAREER Development Program, which recognizes and supports the early career-development activities of those teacher-scholars who are most likely to become the academic
leaders of the 21st century. Henry is also a member of the National Bureau of Economic Research (NBER), a nonpartisan economics
think tank based in Cambridge, Massachusetts.
Peter Blair Henry’s love of learning and his questioning nature have led him to his desired career as an international economist
whose research positively impacts and addresses the tough decisions that face the world’s economies. It is his foundation in mathematics that enables him to grapple objectively with complex and emotionally charged issues of international economic policy
reform, such as debt relief for developing countries and its effect on international stock markets. The equation on this cover comes
from a paper that investigates the economic impact of a country’s decision to open its stock market to foreign investors. The paper
uses data on investment and stock prices in an attempt to answer vital questions at the frontier of current research on an important
issue for developing countries.*

Look for other featured applied researchers in forthcoming titles in the Tan applied mathematics series:

CHRIS SHANNON
Economics and Finance
University of California,
Berkeley

MARK VAN DER LAAN
Biostatistician
University of California,
Berkeley

JONATHAN D. FARLEY
Applied Mathematician
Massachusetts Institute of
Technology

NAVIN KHANEJA
Applied Scientist
Harvard University

*The reference for the paper is Chari, Anusha and Peter Blair Henry “Is the Invisible Hand Discerning or Indiscriminate? Investment and
Stock Prices in the Aftermath of Capital Account Liberalizations,” NBER Working Paper, Number 10318.


LIST OF APPLICATIONS
BUSINESS AND ECONOMICS
401(K) investors, 315
Accumulated value of an income stream, 498
Accumulation years of baby boomers, 197

Advertising, 86, 150, 239, 278, 329, 543, 575
Ailing financial institutions, 129, 147
Aircraft structural integrity, 259
Air travel, 390
Alternative energy sources, 461
Alternative minimum tax, 281, 337
Amusement park attendance, 196, 497
Annual retail sales, 95, 154
Annuities, 359, 391, 475
Assembly time of workers, 278, 383, 434
Authentication technology, 580
Auto financing, 445
Auto replacement parts market, 89
Average age of cars in U.S., 300
Banking, 56, 147, 405
Black Monday, 285
Blackberry subscribers, 87
Book design, 91, 323
Box office receipts, 114, 181, 296
Broadband Internet households, 61
Budget deficit and surplus, 68, 252
Business spending on technology, 281
Cable ad revenue, 96
Cable TV subscription, 244, 407, 418, 448
Capital value, 521
Cargo volume, 266
Cash reserves at Blue Cross and Blue Shield, 282
CDs, 351, 489
Cellular phone subscription, 262
Charter-flight revenue, 84, 92

Chip sales, 87
City planning, 118, 182
Coal production, 447, 489
Cobb-Douglas production function, 556, 557, 590,
593, 610
COLAs, 61
Commissions, 130
Commodity prices, 130, 158, 368, 489
Common stock transactions, 4, 358
Commuter airlines, 488
Compact disc sales, 489
Comparison of bank rates, 359
Complementary commodities, 553, 558
Computer game sales, 535
Computer resale value, 480
Construction jobs, 76, 103, 184
Consumer decisions, 30
Consumer demand, 168, 181, 245, 394
Consumer price index, 169, 273, 394
Consumers’ surplus, 467, 473, 474, 476, 477, 481,
497, 502, 511
Consumption function, 61
Consumption of electricity, 435
Consumption of petroleum, 509
Cost of laying cable, 26, 30
Cost of producing calculators, 329
Cost of producing guitars, 406
Cost of producing loudspeakers, 303

Cost of producing PDAs, 75

Cost of producing solar cell panels, 414
Cost of producing surfboards, 150
Cost of removing toxic waste, 181, 296
Cost of wireless phone calls, 245
Creation of new jobs, 195
Credit card debt, 88, 407
Crop yield, 148, 371
Cruise ship bookings, 195
Demand for agricultural commodities, 239
Demand for butter, 531
Demand for computer software, 535
Demand for DVDs, 576
Demand for digital camcorder tapes, 481
Demand for electricity, 582
Demand for perfume, 367
Demand for personal computers, 195, 387
Demand for RNs, 279
Demand for videocassettes, 83
Demand for wine, 368
Demand for wristwatches, 181, 195
Depletion of Social Security funds, 315
Depreciation, 88, 365, 448
Designing a cruise ship pool, 589
Determining the optimal site, 570
Digital camera sales, 168
Digital TV sales, 280
Digital TV services, 44
Digital TV shipments, 95
Digital vs film cameras, 88
Disability benefits, 217

Disposable annual incomes, 86
Document management, 87
Driving costs, 81, 114, 154
Driving range of an automobile, 10
Drug spending, 281
DVD sales, 176, 407
Effect of advertising on bank deposits, 278
Effect of advertising on hotel revenue, 281
Effect of advertising on profit, 150, 239
Effect of advertising on sales, 86, 169, 235, 273, 387,
461
Effect of housing starts on jobs, 195
Effect of inflation on salaries, 359
Effect of luxury tax on consumption, 194
Effect of mortgage rates on housing starts, 75, 239
Effect of price increase on quantity demanded, 239,
242
Effect of speed on operating cost of a truck, 235
Effect of TV advertising on car sales, 461
Efficiency studies, 169, 280, 438
Elasticity of demand, 205, 208, 210, 211, 230
E-mail usage, 87
Energy conservation, 452, 460
Energy consumption and productivity, 130, 358
Energy efficiency of appliances, 367
Establishing a trust fund, 521
Expected demand, 394
Expressway tollbooths, 532
Federal budget deficit, 68, 252
Federal debt, 96, 314

Female self-employed workforce, 309

Financing a college education, 359, 475
Financing a home, 239, 241
Forecasting commodity prices, 239
Forecasting profits, 239, 281
Forecasting sales, 158, 416
Franchises, 475, 498
Frequency of road repairs, 531
Fuel consumption of domestic cars, 510
Fuel economy of cars, 172, 248
Gasoline prices, 291
Gasoline self-service sales, 57
Gas station sales, 531
Gender gap, 60
Google’s revenue, 282
Gross domestic product, 150, 166, 217, 239, 276, 311
Growth of bank deposits, 56
Growth of HMOs, 173, 490
Growth of managed services, 261
Growth of service industries, 512
Growth of Web sites, 336
Health-care costs, 170, 407
Health club membership, 158, 189
Home mortgages, 545, 546
Home sales, 173
Home-shopping industry, 135
Hotel occupancy rate, 75, 89, 194
Households with microwaves, 389
Housing prices, 358, 447

Housing starts, 76, 195, 225
Illegal ivory trade, 88
Income distribution of a country, 481
Income streams, 468, 519
Incomes of American families, 370
Indian gaming industry, 94
Inflation, 215
Information security software sales, 578
Installment contract sales, 481
Inventory control and planning, 129, 321, 322, 325,
329, 330
Investment analysis, 359, 469, 475
Investment options, 358
Investment returns, 240, 358, 394
IRAs, 470
Keogh accounts, 240, 481
Land prices, 557, 570, 606
Life span of color television tubes, 531
Life span of light bulbs, 525, 528
Linear depreciation, 61, 88
Loan amortization, 370, 545, 546
Loan consolidation, 358
Loans at Japanese banks, 367
Locating a TV relay station, 568
Lorentz curves, 472, 475, 498
Magazine circulation, 403
Management decisions, 281, 469
Manufacturing capacity, 67, 173, 266, 284
Manufacturing capacity operating rate, 307
Manufacturing costs, 74

Marginal average cost function, 200, 201, 209, 210
Marginal cost function, 198, 199, 209, 210, 437, 480
Marginal productivity of labor and capital, 552
Marginal productivity of money, 591

(continued)


List of Applications (continued)
Marginal profit, 203, 209, 210
Marginal propensity to consume, 210
Marginal propensity to save, 210
Marginal revenue, 203, 209, 210, 311, 367, 480
Market equilibrium, 83, 91, 95, 157, 158, 466
Market for cholesterol-reducing drugs, 78
Market for drugs, 579, 583
Market share, 148, 404
Markup on a car, 10
Mass transit subsidies, 578
Maximizing crop yield, 323
Maximizing oil production, 368
Maximizing production, 593
Maximizing profit, 303, 309, 310, 328, 329, 567, 569,
576, 588, 591, 592
Maximizing revenue, 310, 324, 367
Maximizing sales, 593
Meeting profit goals, 10
Meeting sales targets, 10
Metal fabrication, 322
Minimizing construction costs, 322, 329, 592, 593

Minimizing container costs, 319, 323, 329, 593
Minimizing costs of laying cable, 324
Minimizing heating and cooling costs, 571
Minimizing packaging costs, 323, 329
Minimizing production costs, 310
Minimizing shipping costs, 29
Morning traffic rush, 267
Mortgage rates, 496
Multimedia sales, 220, 285
Navigation systems, 44, 48
Net investment flow, 448
Net sales, 578
New construction jobs, 184
Newsmagazine shows, 418
Nielsen television polls, 134, 147
Office rents, 311
Oil production, 448, 460, 481, 487
Oil spills, 230, 506, 535
Online ad sales, 407
Online banking, 366, 390
Online buyers, 168, 377
Online hotel reservations, 328
Online retail sales, 358
Online sales of used autos, 579
Online shopping, 96
Online spending, 96, 579
Operating costs of a truck, 235
Operating rates of factories, mines, and utilities, 307
Optimal charter flight fare, 324
Optimal market price, 364

Optimal selling price, 368
Optimal speed of a truck, 325
Optimal subway fare, 318
Outpatient service companies, 408
Outsourcing of jobs, 87, 193, 281
Ownership of portable phones, 168
Packaging, 52, 91, 317, 319, 329, 570, 571
PC shipments, 281
Pensions, 358, 359
Perpetual net income stream, 521
Perpetuities, 535
Personal consumption expenditure, 210
Portable phone services, 168, 580
Present value of a franchise, 490
Present value of an income stream, 475
Prime interest rate, 130
Producers’ surplus, 467, 473, 474, 476, 481, 497, 511,
535
Product design, 323

Product reliability, 531
Production costs, 208, 209, 433
Production of steam coal, 489
Productivity of a country, 557
Productivity fueled by oil, 368
Profit of a vineyard, 92, 325
Projected Provident funds, 262
Projection TV sales, 480
Purchasing power, 358
Quality control, 10, 406

Racetrack design, 325
Rate of bank failures, 220, 266, 314
Rate of change of DVD sales, 176
Rate of change of housing starts, 225
Rate of return on investment, 358, 490
Real estate, 355, 359, 428, 447, 510
Reliability of computer chips, 387
Reliability of microprocessors, 532
Reliability of robots, 531
Resale value, 387
Retirement planning, 358, 359, 481
Revenue growth of a home theater business, 358
Revenue of a charter yacht, 324
Reverse annuity mortgage, 475
Sales forecasts, 51
Sales growth and decay, 44
Sales of digital signal processors, 95, 169
Sales of digital TVs, 86
Sales of drugs, 582
Sales of DVD players vs VCRs, 89
Sales of functional food products, 262
Sales of GPS equipment, 579
Sales of mobile processors, 281
Sales of pocket computers, 438
Sales of prerecorded music, 60
Sales of a sporting good store, 38
Sales of video games, 535
Sales promotions, 367
Sales tax, 61
Satellite radio subscriptions, 406

Selling price of DVD recorders, 87, 193
Shopping habits, 531
Sickouts, 314
Sinking funds, 471
Social Security beneficiaries, 136
Social Security contributions, 43
Social Security wage base, 579
Solvency of the Social Security system, 299, 315
Spending on Medicare, 169
Starbucks’ annual sales, 582
Starbucks’ store count, 578
Stock purchase, 4
Substitute commodities, 553, 558, 610
Supply and demand, 83, 90, 168, 226, 230, 418
Tax planning, 358
Testing new products, 217
Time on the market, 285, 314
Tread-lives of tires, 512
Truck leasing, 61
Trust funds, 525
TV-viewing patterns, 134, 193
VCR ownership, 497
Use of diesel engines, 314
Value of an art object, 39
Value of an investment, 74
U.S. daily oil consumption, 511
U.S. drug sales, 579
U.S. nutritional supplements market, 88
U.S. online banking households, 579
U.S. strategic petroleum reserves, 511

Venture-capital investment, 311
Wages, 145
Web hosting, 262
Wilson lot size formula, 546
Worker efficiency, 62, 86, 169, 280, 329
World production of coal, 447, 481
Worldwide production of vehicles, 197
Yahoo! in Europe, 377
Yield of an apple orchard, 91

SOCIAL SCIENCES
Age of drivers in crash fatalities, 263
Aging drivers, 86
Aging population, 193, 218, 617
Air pollution, 194, 262, 263, 267, 282, 408, 511
Air purification, 217
Alcohol-related traffic accidents, 489
Annual college costs, 583
Arson for profit, 545
Bursts of knowledge, 124
Continuing education enrollment, 194
Closing the gender gap in education, 61
College admissions, 43, 578
Commuter trends, 480
Continuing education enrollment, 194
Cost of removing toxic waste, 114, 178, 181, 296
Crime, 217, 239, 257, 311
Cube rule, 62
Curbing population growth, 170

Decline of union membership, 67
Demographics, 388
Dependency ratio, 282
Disability benefits, 217
Disability rates, 336
Dissemination of information, 388
Distribution of incomes, 10, 360, 473, 475
Educational level of senior citizens, 40, 577
Effect of budget cuts on crime rate, 280
Effect of smoking bans, 280
Elderly workforce, 262
Endowments, 519, 521
Energy conservation, 456
Energy needs, 435
Family vs annual income, 360
Female life expectancy, 192, 418, 610
Food stamp recipients, 315
Foreign-born residents, 311
Gender gap, 60
Global epidemic, 440
Global supply of plutonium, 75
Growth of HMOs, 173, 284
Health-care spending, 73, 170
HMOs, 79
Immigration, 89, 386
Income distributions, 473
Increase in juvenile offenders, 371
Index of environmental quality, 329
Intervals between phone calls, 532
Lay teachers at Roman Catholic schools, 385, 391

Learning curves, 124, 129, 181, 239, 387, 418
Logistic curves, 385
Male life expectancy, 245, 580
Marijuana arrests, 96, 440
Married households, 336
Married households with children, 168
Mass transit, 318, 578
Medical school applicants, 262
Membership in credit unions, 448
Narrowing gender gap, 44
Nuclear plant utilization, 43

(continued on back endpaper)


BASIC RULES OF DIFFERENTIATION
d
1. ᎏᎏ (c) ϭ 0,
dx

c a constant

d
du
2. ᎏᎏ (un) ϭ nunϪ1ᎏᎏ
dx
dx
d
d√
du

3. ᎏᎏ (u Ϯ √) ϭ ᎏᎏ Ϯ ᎏᎏ
dx
dx
dx
d
du
4. ᎏᎏ (cu) ϭ c ᎏᎏ,
dx
dx

c a constant

d
d√
du
5. ᎏᎏ (u√) ϭ u ᎏᎏ ϩ √ ᎏᎏ
dx
dx
dx
d√
du
√ ᎏᎏ Ϫ u ᎏᎏ
dx
dx
d u
6. ᎏᎏ !ᎏᎏ@ ϭ ᎏᎏ
√2
dx √
d
du

7. ᎏᎏ (eu) ϭ eu ᎏᎏ
dx
dx
d
1 du
8. ᎏᎏ (ln u) ϭ ᎏᎏ и ᎏᎏ
dx
u dx

BASIC RULES OF INTEGRATION
1. µ du ϭ u ϩ C
2. µ k f (u) du ϭ k µ f(u) du,

k a constant

3. µ [ f (u) Ϯ g(u)] du ϭ µ f (u) du Ϯ µ g(u) du
unϩ1
4. µ un du ϭ ᎏᎏ ϩ C,
nϩ1
5. µ eu du ϭ eu ϩ C
du
6. µ ᎏᎏ ϭ ln͉u͉ ϩ C
u

n

Ϫ1


Calculus

for the Managerial, Life,
and Social Sciences
Seventh Edition


This page intentionally left blank


Calculus
for the Managerial, Life,
and Social Sciences
Seventh Edition

S. T. TAN
STONEHILL COLLEGE

Australia • Canada • Mexico • Singapore • Spain
United Kingdom • United States


Executive Publisher: Curt Hinrichs
Development Editor: Danielle Derbenti
Senior Assistant Editor: Ann Day
Editorial Assistant: Fiona Chong
Technology Project Manager: Earl Perry
Marketing Manager: Tom Ziolkowski
Marketing Assistant: Jessica Bothwell
Advertising Project Manager: Nathaniel Bergson-Michelson
Project Manager, Editorial Production: Sandra Craig
Art Director: Lee Friedman

Print/Media Buyer: Doreen Suruki

Permissions Editor: Sarah Harkrader
Production: Cecile Joyner, The Cooper Company
Text Designer: Diane Beasley
Photo Researcher: Stephen Forsling
Copy Editor: Betty Duncan
Illustrator: Better Graphics, Inc.; Accurate Art
Cover Designer: Irene Morris
Cover Image: Portrait of Peter Blair Henry by Peter Kiar
Cover Printer: Phoenix Color Corp
Compositor: Better Graphics, Inc.
Printer: R. R. Donnelley/Willard

© 2006 Thomson Brooks/Cole, a part of The Thomson Corporation.
Thomson, the Star logo, and Brooks/Cole are trademarks used herein
under license.

Thomson Higher Education
10 Davis Drive
Belmont, CA 94002-3098
USA

ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means—
graphic, electronic, or mechanical, including photocopying, recording,
taping, Web distribution, information storage and retrieval systems, or in
any other manner—without the written permission of the publisher.
Printed in the United States of America
1 2 3 4 5 6 7 09 08 07 06 05

For more information about our products, contact us at:
Thomson Learning Academic Resource Center
1-800-423-0563
For permission to use material from this text or product,
submit a request online at .
Any additional questions about permissions
can be submitted by email to


© 2006 Thomson Learning, Inc. All Rights Reserved. Thomson Learning
WebTutorTM is a trademark of Thomson Learning, Inc.
Library of Congress Control Number: 2004114814
Student Edition: ISBN 0-534-41986-0
Instructor’s Edition: ISBN 0-534-42000-1
International Student Edition: ISBN: 0-495-01533-4
(Not for sale in the United States)

Asia (including India)
Thomson Learning
5 Shenton Way
#01-01 UIC Building
Singapore 068808
Australia/New Zealand
Thomson Learning Australia
102 Dodds Street
Southbank, Victoria 3006
Australia
Canada
Thomson Nelson
1120 Birchmount Road

Toronto, Ontario M1K 5G4
Canada
UK/Europe/Middle East/Africa
Thomson Learning
High Holborn House
50/51 Bedford Row
London WC1R 4LR
United Kingdom
Latin America
Thomson Learning
Seneca, 53
Colonia Polanco
11560 Mexico
D.F. Mexico
Spain (including Portugal)
Thomson Paraninfo
Calle Magallanes, 25
28015 Madrid, Spain


TO PAT, BILL, AND MICHAEL


Contents

Preface x
CHAPTER 1

Preliminaries 1
1.1

1.2
1.3
1.4

CHAPTER 2

Precalculus Review I 2
Precalculus Review II 11
The Cartesian Coordinate System 23
Straight Lines 31
Chapter 1 Summary of Principal Formulas and Terms 46
Chapter 1 Concept Review Questions 46
Chapter 1 Review Exercises 47
Chapter 1 Before Moving On 48

Functions, Limits, and the Derivative 49
2.1
2.2
2.3
2.4
2.5
2.6

CHAPTER 3

Functions and Their Graphs 50
Using Technology: Graphing a Function 64
The Algebra of Functions 68
Functions and Mathematical Models 76
Using Technology: Finding the Points of Intersection of Two Graphs and Modeling 93

Limits 97
Using Technology: Finding the Limit of a Function 116
One-Sided Limits and Continuity 119
Using Technology: Finding the Points of Discontinuity of a Function 132
Derivative 135
Using Technology: Graphing a Function and Its Tangent Line 152
Chapter 2 Summary of Principal Formulas and Terms 155
Chapter 2 Concept Review Questions 155
Chapter 2 Review Exercises 156
Chapter 2 Before Moving On 158

Differentiation 159
3.1

Basic Rules of Differentiation 160
Using Technology: Finding the Rate of Change of a Function 171
*Sections marked with an asterisk are not prerequisites for later material.

vi


CONTENTS

3.2
3.3
3.4
3.5

The Product and Quotient Rules 174
Using Technology: The Product and Quotient Rules 183

The Chain Rule 185
Using Technology: Finding the Derivative of a Composite Function 196
Marginal Functions in Economics 197
Higher-Order Derivatives 212
PORTFOLIO: Steve Regenstreif 213

*3.6
3.7

CHAPTER 4

Using Technology: Finding the Second Derivative of a Function at a Given Point 219
Implicit Differentiation and Related Rates 221
Differentials 232
Using Technology: Finding the Differential of a Function 240
Chapter 3 Summary of Principal Formulas and Terms 242
Chapter 3 Concept Review Questions 243
Chapter 3 Review Exercises 243
Chapter 3 Before Moving On 245

Applications of the Derivative 247
4.1
4.2
4.3
4.4
4.5

CHAPTER 5

Applications of the First Derivative 248

Using Technology: Using the First Derivative to Analyze a Function 264
Applications of the Second Derivative 267
Using Technology: Finding the Inflection Points of a Function 283
Curve Sketching 285
Using Technology: Analyzing the Properties of a Function 298
Optimization I 300
Using Technology: Finding the Absolute Extrema of a Function 313
Optimization II 315
Chapter 4 Summary of Principal Terms 327
Chapter 4 Concept Review Questions 327
Chapter 4 Review Exercises 328
Chapter 4 Before Moving On 330

Exponential and Logarithmic Functions 331
5.1
5.2
5.3
5.4

Exponential Functions 332
Using Technology 338
Logarithmic Functions 339
Compound Interest 347
Differentiation of Exponential Functions 360
PORTFOLIO: Robert Derbenti 361

5.5
*5.6

Using Technology 370

Differentiation of Logarithmic Functions 371
Exponential Functions as Mathematical Models 379
Using Technology: Analyzing Mathematical Models 389
Chapter 5 Summary of Principal Formulas and Terms 392
Chapter 5 Concept Review Questions 392

vii


viii

CONTENTS

Chapter 5 Review Exercises 393
Chapter 5 Before Moving On 394

CHAPTER 6

Integration 395
6.1
6.2
6.3
6.4
6.5
6.6
*6.7

CHAPTER 7

Antiderivatives and the Rules of Integration 396

Integration by Substitution 410
Area and the Definite Integral 420
The Fundamental Theorem of Calculus 429
Using Technology: Evaluating Definite Integrals 440
Evaluating Definite Integrals 441
Using Technology: Evaluating Definite Integrals for Piecewise-Defined Functions 450
Area between Two Curves 452
Using Technology: Finding the Area between Two Curves 463
Applications of the Definite Integral to Business and Economics 464
Using Technology: Business and Economic Applications 476
Chapter 6 Summary of Principal Formulas and Terms 478
Chapter 6 Concept Review Questions 479
Chapter 6 Review Exercises 479
Chapter 6 Before Moving On 482

Additional Topics in Integration 483
7.1
* 7.2
* 7.3
7.4
*7.5

Integration by Parts 484
Integration Using Tables of Integrals 491
Numerical Integration 498
Improper Integrals 513
Applications of Calculus to Probability 522
PORTFOLIO: Gary Li 530

Chapter 7 Summary of Principal Formulas and Terms 533

Chapter 7 Concept Review Questions 534
Chapter 7 Review Exercises 534
Chapter 7 Before Moving On 536

CHAPTER 8

Calculus of Several Variables 537
8.1
8.2
8.3

Functions of Several Variables 538
Partial Derivatives 547
Using Technology: Finding Partial Derivatives at a Given Point 560
Maxima and Minima of Functions of Several Variables 561
PORTFOLIO: Kirk Hoiberg 564

8.4
8.5
8.6

The Method of Least Squares 572
Using Technology: Finding an Equation of a Least-Squares Line 581
Constrained Maxima and Minima and the Method of Lagrange Multipliers 583
Double Integrals 594


CONTENTS

Chapter 8 Summary of Principal Formulas and Terms 608

Chapter 8 Concept Review Questions 608
Chapter 8 Review Exercises 609
Chapter 8 Before Moving On 610

APPENDIX

Inverse Functions 611
Answers to Odd-Numbered Exercises 619
Index 661

ix


Preface

M

ath is an integral part of our increasingly complex daily life. Calculus for the
Managerial, Life, and Social Sciences, Seventh Edition, attempts to illustrate this
point with its applied approach to mathematics. Our objective for this Seventh
Edition is twofold: (1) to write an applied text that motivates students and (2) to
make the book a useful teaching tool for instructors. We hope that with the present
edition we have come one step closer to realizing our goal. This book is suitable for
use in a one-semester or two-quarter introductory calculus course for students in the
managerial, life, and social sciences.

Features of the Seventh Edition
■

■

Coverage of Topics This text offers more than enough material for the usual
applied calculus course. Optional sections have been marked with an asterisk in
the table of contents, thereby allowing the instructor to be flexible in choosing the
topics most suitable for his or her course.
Level of Presentation Our approach is intuitive, and we state the results informally. However, we have taken special care to ensure that this approach does not
compromise the mathematical content and accuracy. Proofs of certain results are
given, but they may be omitted if desired.

Intuitive Approach The author motivates each mathematical concept with a reallife example that students can relate to. An illustrative list of some of the topics
introduced in this manner follows:
■

■
■
■
■
■
■
■
■
■

Limits This concept is introduced with the Motion of a Maglev example. Later,
the same example is used to illustrate the concept of a derivative, the intermediate value theorem, and antiderivatives and at the same time show the connection
between all of these concepts.
Algebra of Functions The U.S. Budget Deficit
Differentials Calculating Mortgage Payments
Increasing and Decreasing Functions The Fuel Economy of a Car
Concavity U.S. and World Population Growth

Inflection Points The Point of Diminishing Returns
Curve Sketching The Dow Jones Industrial Average on Black Monday
Exponential Functions Income Distribution of American Families
Area between Two Curves Petroleum Saved with Conservation Measures
Approximating Definite Integrals The Cardiac Output of a Heart

Applications
real world.
■

x

The applications show the connection between mathematics and the

Current and Relevant Examples and Exercises are drawn from the fields of
business, economics, social and behavioral sciences, life sciences, physical sci-


PREFACE

xi

ences, and other fields of general interest. In the examples, these are highlighted
with new icons that illustrate the various applications.

APPLIED EXAMPLE 3 Optimal Subway Fare A city’s Metropolitan
Transit Authority (MTA) operates a subway line for commuters from a certain suburb to the downtown metropolitan area. Currently, an average of 6000
passengers a day take the trains, paying a fare of $3.00 per ride. The board of
the MTA, contemplating raising the fare to $3.50 per ride in order to generate a
larger revenue, engages the services of a consulting firm. The firm’s study reveals

that for each $.50 increase in fare, the ridership will be reduced by an average of
1000 passengers a day. Thus, the consulting firm recommends that MTA stick to
the current fare of $3.00 per ride, which already yields a maximum revenue.
Show that the consultants are correct.

■

New Applications More than 100 new real-life applications have been introduced. Among these applications are Sales of GPS Equipment, Broadband
Internet Households, Cancer Survivors, Spam Messages, Global Supply of
Plutonium, Testosterone Use, Blackberry Subscribers, Outsourcing of Jobs,
Spending on Medicare, Obesity in America, U.S. Nursing Shortage, Effects of
Smoking Bans, Google’s Revenue, Computer Security, Yahoo! in Europe,
Satellite Radio Subscriptions, Gastric Bypass Surgeries, and the Surface Area of
the New York Central Park Reservoir.

66. OUTSOURCING OF JOBS According to a study conducted in
2003, the total number of U.S. jobs that are projected to leave
the country by year t, where t ϭ 0 corresponds to 2000, is
N(t) ϭ 0.0018425(t ϩ 5)2.5

(0 Յ t Յ 15)

where N(t) is measured in millions. How fast will the number of U.S. jobs that are outsourced be changing in 2005? In
2010 (t ϭ 10)?
Source: Forrester Research

■

New Portfolios are designed to convey to the student the real-world experiences
of professionals who have a background in mathematics and use it in their daily

business interactions.


xii

PREFACE

530

7 ADDITIONAL

PORTFOLIO Gary Li
TITLE Associate
INSTITUTION JPMorgan Chase
As one of the leading financial
institutions in the world, JPMorgan
Chase & Co. depends on a wide
range of mathematical disciplines
from statistics to linear programming to calculus. Whether assessing the credit worthiness
of a borrower, recommending portfolio investments or
pricing an exotic derivative, quantitative understanding is
a critical tool in serving the financial needs of clients.
I work in the Fixed-Income Derivatives Strategy
group. A derivative in finance is an instrument whose
value depends on the price of some other underlying
instrument. A simple type of derivative is the forward
contract, where two parties agree to a future trade at a
specified price. In agriculture, for instance, farmers will
often pledge their crops for sale to buyers at an agreed
price before even planting the harvest. Depending on the

weather, demand and other factors, the actual price may
turn out higher or lower. Either the buyer or seller of the
f
d
b fi
di l
h
l
f h
■

with interest rates. With trillions of dollars in this form,
especially government bonds and mortgages, fixedincome derivatives are vital to the economy. As a strategy
group, our job is to track and anticipate key drivers and
developments in the market using, in significant part,
quantitative analysis. Some of the derivatives we look at
are of the forward kind, such as interest-rate swaps, where
over time you receive fixed-rate payments in exchange for
paying a floating-rate or vice-versa. A whole other class
of derivatives where statistics and calculus are especially
relevant are options.
Whereas forward contracts bind both parties to a
future trade, options give the holder the right but not the
obligation to trade at a specified time and price. Similar to
an insurance policy, the holder of the option pays an
upfront premium in exchange for potential gain. Solving
this pricing problem requires statistics, stochastic calculus
and enough insight to win a Nobel prize. Fortunately for
us, this was taken care of by Fischer Black, Myron
S h l

d R b t M t i th
l 1970 (i l di

Explore & Discuss boxes, appearing throughout the main body of the text, offer
optional questions that can be discussed in class or assigned as homework. These
questions generally require more thought and effort than the usual exercises. They
may also be used to add a writing component to the class, giving students opportunities to articulate what they have learned. Complete solutions to
these exercises are given in the Instructor’s Solutions Manual.

EXPLORE & DISCUSS
The profit P of a one-product software manufacturer depends on the number of units
of its products sold. The manufacturer estimates that it will sell x units of its product
per week. Suppose P ϭ g(x) and x ϭ f(t), where g and f are differentiable functions.
1. Write an expression giving the rate of change of the profit with respect to the number of units sold.
2. Write an expression giving the rate of change of the number of units sold per week.
3. Write an expression giving the rate of change of the profit per week.

Real-Life Data Many of the applications are based on mathematical models (functions) that have been constructed using data drawn from various sources including
current newspapers and magazines, and data obtained through the Internet. Sources
are given in the text for these applied problems. In Functions and Mathematical
Models (Section 2.3), the modeling process is discussed and students are asked to


PREFACE

xiii

use models (functions) constructed from real-life data to answer questions about the
Market for Cholesterol-Reducing Drugs, HMO Membership, and the Driving Costs
for a Ford Taurus. In the Using Technology section that follows, students learn how

to construct a function describing the growth of the Indian Gaming Industry using a
graphing calculator. Hands-on experience constructing models from other real-life
data is provided by the exercises that follow.
Exercise Sets The exercise sets are designed to help students understand and apply
the concepts developed in each section. Three types of exercises are included in
these sets:
■

■

■

3.3

Self-Check Exercises offer students immediate feedback on key concepts with
worked-out solutions following the section exercises.
New Concept Questions are designed to test students’ understanding of the basic
concepts discussed in the section and at the same time encourage students to
explain these concepts in their own words.
Exercises provide an ample set of problems of a routine computational nature followed by an extensive set of application-oriented problems.

Self-Check Exercises

1. Find the derivative of
1
f(x) ϭ Ϫ ᎏ
œෆ
2x 2 Ϫෆ
1
2. Suppose the life expectancy at birth (in years) of a female in a

certain country is described by the function
g(t) ϭ 50.02(1 ϩ 1.09t)0.1

3.3

(0 Յ t Յ 150)

Solutions to Self-Check Exercises 3.3 can be found on
page 196.

Concept Questions

1. In your own words, state the chain rule for differentiating the
composite function h(x) ϭ g[ f (x)].

3.3

where t is measured in years, with t ϭ 0 corresponding to the
beginning of 1900.
a. What is the life expectancy at birth of a female born at the
beginning of 1980? At the beginning of 2000?
b. How fast is the life expectancy at birth of a female born at
any time t changing?

2. State the general power rule for differentiating the function
h(x) ϭ [ f (x)]n, where n is a real number.

Exercises

In Exercises 1–48, find the derivative of each function.

29. f(x) ϭ 2x 2(3 Ϫ 4x)4

30. h(t) ϭ t 2(3t ϩ 4)3

1. f(x) ϭ (2x Ϫ 1)

2. f(x) ϭ (1 Ϫ x)

31. f(x) ϭ (x Ϫ 1)2(2x ϩ 1)4

3. f(x) ϭ (x 2 ϩ 2)5

4. f(t) ϭ 2(t 3 Ϫ 1)5

32. g(u) ϭ (1 ϩ u2)5(1 Ϫ 2u2)8

5. f(x) ϭ (2x Ϫ x 2)3

6. f(x) ϭ 3(x 3 Ϫ x)4

7. f(x) ϭ (2x ϩ 1)Ϫ2

1
8. f(t) ϭ ᎏᎏ(2t 2 ϩ t)Ϫ3
2

xϩ3 3
33. f(x) ϭ !ᎏᎏ@
xϪ2

xϩ1 5
34. f(x) ϭ !ᎏᎏ@
xϪ1

3/2
t
35. s(t) ϭ !ᎏᎏ@
2t ϩ 1

1 3/2
36. g(s) ϭ !s2 ϩ ᎏᎏ@
s

4

9. f(x) ϭ (x 2 Ϫ 4)3/2
11. f(x) ϭ œෆ
3x Ϫ 2

3

10. f(t) ϭ (3t 2 Ϫ 2t ϩ 1)3/2
12. f(t) ϭ œෆ
3t 2 Ϫ tෆ

37. g(u) ϭ

u ϩ1

ᎏ
Ίᎏ
๶
3
2

38. g(x) ϭ

2x ϩ 1

ᎏ
Ίᎏ
๶
2
1


xiv

PREFACE

3.3

Solutions to Self-Check Exercises
or approximately 78 yr. Similarly, the life expectancy at
birth of a female born at the beginning of the year 2000 is
given by

1. Rewriting, we have
f(x) ϭ Ϫ(2x 2 Ϫ 1)Ϫ1/2

g(100) ϭ 50.02[1 ϩ 1.09(100)]0.1 Ϸ 80.04

Using the general power rule, we find
d
f Ј(x) ϭ Ϫᎏᎏ (2x 2 Ϫ 1)Ϫ1/2
dx
1
d
ϭ Ϫ!Ϫᎏᎏ@(2x 2 Ϫ 1)Ϫ3/2 ᎏᎏ(2x 2 Ϫ 1)
2
dx
1
ϭ ᎏᎏ(2x 2 Ϫ 1)Ϫ3/2(4x)
2
2x
ϭᎏ
ᎏ
(2x 2 Ϫ 1)3/2
2. a. The life expectancy at birth of a female born at the beginning of 1980 is given by
g(80) ϭ 50.02[1 ϩ 1.09(80)]0.1 Ϸ 78.29

or approximately 80 yr.
b. The rate of change of the life expectancy at birth of a
female born at any time t is given by gЈ(t). Using the general power rule, we have
d
gЈ(t) ϭ 50.02ᎏᎏ(1 ϩ 1.09t)0.1
dt
d
ϭ (50.02)(0.1)(1 ϩ 1.09t)Ϫ0.9ᎏᎏ(1 ϩ 1.09t)

dt
ϭ (50.02)(0.1)(1.09)(1 ϩ 1.09t)Ϫ0.9
ϭ 5.45218(1 ϩ 1.09t)Ϫ0.9
5.45218
ϭ ᎏᎏ
(1 ϩ 1.09t)0.9

Review Sections These sections are designed to help students review the material
in each section and assess their understanding of basic concepts as well as problemsolving skills.
■

■

■

■

CHAPTER

2

Summary of Principal Formulas and Terms highlights important equations and
terms with page numbers given for quick review.
New Concept Review Questions give students a chance to check their knowledge of the basic definitions and concepts given in each chapter.
Review Exercises offer routine computational exercises followed by applied
problems.
New Before Moving On . . . Exercises give students a chance to see if they have
mastered the basic computational skills developed in each chapter. If they solve a
problem incorrectly, they can go to the companion Website and try again. In fact,
they can keep on trying until they get it right. If students need step-by-step help,

they can utilize the iLrn Tutorials that are keyed to the text and work out similar
problems at their own pace.

Summary of Principal Formulas and Terms

FORMULAS
1. Average rate of change of f over
[x, x ϩ h] or
Slope of the secant line to the
graph of f through (x, f(x)) and
(x ϩ h, f(x ϩ h)) or
Difference quotient

f(x ϩ h) Ϫ f(x)
ᎏᎏ
h


PREFACE

TERMS
function (50)

polynomial function (80)

limit of a function (100)

domain (50)

linear function (80)

indeterminate form (103)

range (50)

quadratic function (80)

limit of a function at infinity (107)

independent variable (51)

cubic function (80)

right-hand limit of a function (119)

dependent variable (51)

rational function (80)

left-hand limit of a function (119)

ordered pairs (53)

power function (81)

continuity of a function at a number (121)

function (alternative definition) (53)

demand function (82)

secant line (137)

graph of a function (53)

supply function (82)

tangent line to the graph of f (137)

graph of an equation (56)

market equilibrium (82)

differentiable function (145)

vertical-line test (56)

equilibrium quantity (82)

composite function (71)

equilibrium price (82)

CHAPTER

2

Concept Review Questions

Fill in the blanks.

1. If f is a function from the set A to the set B, then A is called
the
of f, and the set of all values of f(x) as x takes on
all possible values in A is called the
of f. The range of
f is contained in the set
.
2. The graph of a function is the set of all points (x, y) in the xyplane such that x is in the
of f and y ϭ
. The
vertical-line test states that a curve in the xy-plane is the graph
of a function y ϭ f(x) if and only if each
line intersects
it in at most one
.
3. If f and g are functions with domains A and B, respectively,
then (a) ( f Ϯ g)(x) ϭ
, (b) ( fg)(x) ϭ
, and (c)
f
ᎏᎏ (x) ϭ
. The domain of f ϩ g is
. The domain
g
f
with the additional condition that g(x) is
of ᎏᎏ is
g
never
.

΂΃

CHAPTER

2

4. The composition of g and f is the function with rule (g Ⴆ f )(x)
ϭ
. Its domain is the set of all x in the domain of
such that
lies in the domain of
.
5. a. A polynomial function of degree n is a function of the
form
.
b. A polynomial function of degree 1 is called a
function; one of degree 2 is called a
function; one
of degree 3 is called a
function.
c. A rational function is a/an
of two
.
d. A power function has the form f(x) ϭ
.
6. The statement lim f(x) ϭ L means that there is a number
xǞa

to

such that the values of
can be made as close
as we please by taking x sufficiently close to
.

Review Exercises

1. Find the domain of each function:
a. f(x) ϭ œ9ෆ
Ϫx

xϩ3
b. f(x) ϭ ᎏ
ᎏ
2x 2 Ϫ x Ϫ 3

2. Let f(x) ϭ 3x 2 ϩ 5x Ϫ 2. Find:
a. f(Ϫ2)
b. f(a ϩ 2)
c. f(2a)
d. f(a ϩ h)
3. Let y 2 ϭ 2x ϩ 1.
a. Sketch the graph of this equation.
b. Is y a function of x? Why?
c. Is x a function of y? Why?

8. lim (3x 2 ϩ 4)(2x Ϫ 1)
xǞϪ1

xϪ3
9. lim ᎏᎏ
xǞ3 x ϩ 4

xϩ3
10. lim ᎏ
ᎏ
xǞ2 x 2 Ϫ 9

x 2 Ϫ 2x Ϫ 3
11. lim ᎏ
ᎏ
xǞϪ2 x 2 ϩ 5x ϩ 6

3
ෆ
12. lim œ2x
Ϫෆ
5

4x Ϫ 3
13. lim ᎏᎏ
xǞ3 œෆ
xϩ1

xϪ1
14. limϩ ᎏᎏ
xǞ1 x(x Ϫ 1)

œෆx Ϫ 1

15. limϪ ᎏᎏ
xǞ1
xϪ1

x2
16. lim ᎏ
ᎏ
xǞϱ x 2 Ϫ 1

xǞ3

xv


xvi

PREFACE

CHAPTER

Before Moving On . . .

2

1. Let
f(x) ϭ

Ϫ2x ϩ 1
2
ϩ2

Ϫ1 Յ x Ͻ 0
0ՅxՅ2

Άx

Find (a) f(Ϫ1), (b) f(0), and (c)
1
ᎏᎏ
xϩ1

x

3
f Óᎏ2ᎏÔ.

x

and g(x) ϭ x ϩ 1. Find the rules for (a)
2. Let f(x) ϭ
f ϩ g, (b) fg, (c) f Ⴆ g, and (d) g Ⴆ f.
2

3. Postal regulations specify that a parcel sent by parcel post may
have a combined length and girth of no more than 108 in.
Suppose a rectangular package that has a square cross section of
x in. ϫ x in. is to have a combined length and girth of exactly
108 in. Find a function in terms of x giving the volume of the
package.

Hint: The length plus the girth is 4x ϩ h (see the accompanying figure).

x 2 ϩ 4x ϩ 3
4. Find lim ᎏ
ᎏ.
xǞϪ1 x 2 ϩ 3x ϩ 2
5. Let
f(x) ϭ

h

x2 Ϫ 1

Άx

3

Ϫ2 Յ x Ͻ 1
1ՅxՅ2

Find (a) lim Ϫ f(x) and (b) lim ϩ f(x). Is f continuous at x ϭ 1?
xǞ1
xǞ1
Explain.
6. Find the slope of the tangent line to the graph of x 2 Ϫ 3x ϩ 1
at the point (1, Ϫ1). What is an equation of the tangent line?

Technology Throughout the text, opportunities to explore mathematics through
technology are given.
■

Exploring with Technology Questions appear throughout the main body of the
text and serve to enhance the student’s understanding of the concepts and theory
presented. Complete solutions to these exercises are given in the Instructor’s
Solutions Manual.
EXPLORING WITH TECHNOLOGY
In the opening paragraph of Section 5.1, we pointed out that the accumulated amount
of an account earning interest compounded continuously will eventually outgrow by
far the accumulated amount of an account earning interest at the same nominal rate but
earning simple interest. Illustrate this fact using the following example.
Suppose you deposit $1000 in account I, earning interest at the rate of 10% per
year compounded continuously so that the accumulated amount at the end of t years is
A1(t) ϭ 1000e0.1t. Suppose you also deposit $1000 in account II, earning simple interest at the rate of 10% per year so that the accumulated amount at the end of t years is
A2(t) ϭ 1000(1 ϩ 0.1t). Use a graphing utility to sketch the graphs of the functions A1
and A2 in the viewing window [0, 20] ϫ [0, 10,000] to see the accumulated amounts
A1(t) and A2(t) over a 20-year period.

■

Using Technology Subsections that offer optional material explaining the use of
graphing calculators as a tool to solve problems in calculus and to construct and analyze mathematical models are placed at the end of appropriate sections. These subsections are written in the traditional example-exercise format, with answers given
at the back of the book. Illustrations showing graphing calculator screens are extensively used. Once again many relevant applications with sourced data are introduced
here. These subsections may be used in the classroom if desired or as material for
self-study by the student. Step-by-step instructions (including keystrokes) for many
popular calculators are now given on the disc that accompanies the text. Written
instructions are also given at the Website.


PREFACE

xvii

USING TECHNOLOGY
EXAMPLE 1 At the beginning of Section 5.4, we demonstrated via a table of values of (e h Ϫ 1)/h for selected values of h the plausibility of the result
eh Ϫ 1
lim ᎏᎏ ϭ 1
h

hǞ0

To obtain a visual confirmation of this result, we plot the graph of
FIGURE T1
The graph of f in the viewing window
[Ϫ1, 1] ϫ [0, 2]

ex Ϫ 1
f(x) ϭ ᎏᎏ
x
in the viewing window [Ϫ1, 1] ϫ [0, 2] (Figure T1). From the graph of f, we see that
f(x) appears to approach 1 as x approaches 0.
The numerical derivative function of a graphing utility will yield the derivative
of an exponential or logarithmic function for any value of x, just as it did for algebraic functions.*
*The rules for differentiating logarithmic functions will be covered in Section 5.5. However, the exercises given here
can be done without using these rules.

TECHNOLOGY EXERCISES
In Exercises 1–6, use the numerical derivative operation to
find the rate of change of f(x) at the given value of x. Give
your answer accurate to four decimal places.
1. f(x) ϭ x 3eϪ1/x; x ϭ Ϫ1

Source: House Budget Committee, House Ways and Means
Committee, and U.S. Census Bureau

2. f(x) ϭ (œxෆ ϩ 1)3/2eϪx; x ϭ 0.5
ෆ;
x xϭ2
3. f(x) ϭ x 3œln
œෆx ln x
4. f(x) ϭ ᎏᎏ; x ϭ 3.2
xϩ1
5. f(x) ϭ eϪx ln(2x ϩ 1); x ϭ 0.5

9. WORLD POPULATION GROWTH Based on data obtained in a
study, the world population (in billions) is approximated by
the function

eϪœxෆ
6. f(x) ϭ ᎏᎏ
;xϭ1
ln(x2 ϩ 1)
7. AN EXTINCTION SITUATION The number of saltwater crocodiles
in a certain area of northern Australia is given by
300eϪ0.024t
P(t) ϭ ᎏ
ᎏ
5eϪ0.024t ϩ 1
a. How many crocodiles were in the population initially?
b. Show that lim P(t) ϭ 0.
tǞϱ

c. Plot the graph of P in the viewing window [0, 200] ϫ
[0, 70].
(Comment: This phenomenon is referred to as an extinction situation.)
8. INCOME OF AMERICAN FAMILIES Based on data, it is estimated that
the number of American families y (in millions) who earned x
thousand dollars in 1990 is related by the equation
y ϭ 0.1584xeϪ0.0000016x

ϩ0.00011x 2Ϫ0.04491x

3

a. Plot the graph of the equation in the viewing window
[0, 150] ϫ [0, 2].
b. How fast is y changing with respect to x when x ϭ 10?
When x ϭ 50? Interpret your results.

(x Ͼ 0)

12
f(t) ϭ ᎏᎏᎏ
1 ϩ 3.74914eϪ1.42804t

(0 Յ t Յ 4)

where t is measured in half centuries, with t ϭ 0 corresponding to the beginning of 1950.
a. Plot the graph of f in the viewing window [0, 5] ϫ [0, 14].
b. How fast was the world population expected to increase
at the beginning of 2000?
Source: United Nations Population Division

10. LOAN AMORTIZATION The Sotos plan to secure a loan of
$160,000 to purchase a house. They are considering a conventional 30-yr home mortgage at 9%/year on the unpaid
balance. It can be shown that the Sotos will have an outstanding principal of
160,000(1.0075360 Ϫ 1.0075x)
B(x) ϭ ᎏᎏᎏᎏ
1.0075360 Ϫ 1
dollars after making x monthly payments of $1287.40.


xviii

PREFACE

■

New Interactive Video Skillbuilder CD, in the back of every new text, contains
hours of video instruction from award-winning teacher Deborah Upton of
Stonehill College. Watch as she walks you through key examples from the text,
step by step—giving you a foundation in the skills that you need to know. Each
example found on the CD is identified by the video icon located in the margin.

APPLIED EXAMPLE 5 Marginal Revenue Functions Suppose the
relationship between the unit price p in dollars and the quantity demanded x
of the Acrosonic model F loudspeaker system is given by the equation
p ϭ Ϫ0.02x ϩ 400

(0 Յ x Յ 20,000)

a. Find the revenue function R.

b. Find the marginal revenue function RЈ.
c. Compute RЈ(2000) and interpret your result.

■

New Graphing Calculator Tutorial, by Larry Schroeder of Carl Sandburg
College, can also be found on the Interactive Video Skillbuilder CD and includes
step-by-step instructions, as well as video lessons.

■

Student Resources on the Web Students and instructors will now have access to
these additional materials at the Companion Website: okscole.
com/tans

■

Review material and practice chapter quizzes and tests
Group projects and extended problems for each chapter
Instructions, including keystrokes, for the procedures referenced in the text for
specific calculators (TI-82, TI-83, TI-85, TI-86, and other popular models)
Coverage of additional topics such as Indeterminate Forms and L’Hôpital’s Rule

■
■

■

Other Changes in the Seventh Edition
■

A More Extensive Treatment of Inverse Functions has now been added to
Appendix A.

■

Other Changes In Functions and Mathematical Models (Section 2.3), a new
model describing the membership of HMOs is now discussed by using the scatter
plot of the real-life data and the graph of the function that describes that data.
Another model describing the driving costs of a Ford Taurus is also presented in
this same fashion. In Section 3.6, an additional applied example illustrating the
solution of related-rates problems has been added. In Section 4.2, an example calling for an interpretation of the first and second derivatives to help sketch the graph
of a function has been added. In Section 6.4, the definite integral as a measure of
net change is now discussed along with a new example giving the Population
Growth in Clark County.

■

A Revised Student Solutions Manual Problem-solving strategies, and additional algebra steps and review for selected problems (identified in the Instructor’s
Solutions Manual) have been added to this supplement.


PREFACE

xix

Teaching Aids
■

■

■

■

Instructor’s Solutions Manual includes solutions to all exercises. ISBN 0-53441990-9
Instructor’s Suite CD contains complete solutions to all exercises, along with
PowerPoint slide presentations and test items for every chapter, in formats compatible with Microsoft Office. ISBN 0-534-41987-9
Printed Test Bank, by Tracy Wang, is available to adopters of the book. ISBN
0-534-42006-0
iLrn Testing, available online or on CD-ROM. iLrn Testing is browser-based
fully integrated testing and course management software. With no need for plugins or downloads, iLrn offers algorithmically generated problem values and
machine-graded free response mathematics. ISBN 0-534-42007-9

Learning Aids
■

■

■

Student Solutions Manual, available to both students and instructors, includes
the solutions to odd-numbered exercises. ISBN 0-534-41988-7
WebTutor Advantage for WebCT & Blackboard, by Larry Schroeder, Carl
Sandburg College, contains expanded online study tools including: step-by-step
lecture notes; student study guide with step-by-step TI-89/92/83/86 and Microsoft
Excel explanations; a quick check interactive student problem for each online
example, with accompanying step-by-step solution and step-by-step TI89/92/83/86 solution; practice quizzes by chapter sections that can be used as electronically graded online exercises, and much more. ISBN for WebCT 0-53442015-X and ISBN for Blackboard 0-534-42014-1
Succeeding in Applied Calculus: Algebra Essentials, by Warren Gordon,
Baruch College—City University of New York, provides a clear and concise algebra review. This text is written so that students in need of an algebra refresher may

have a convenient source for reference and review. This text may be especially
useful before or while taking most college-level quantitative courses, including
applied calculus and economics. ISBN 0-534-40122-8

Acknowledgments
I wish to express my personal appreciation to each of the following reviewers of this
Seventh Edition, whose many suggestions have helped make a much improved
book.
Faiz Al-Rubaee
University of North Florida
Albert Bronstein
Purdue University
Kimberly Jordan Burch
Montclair State University
Peter Casazza
University of Missouri—Columbia
Lisa Cox
Texas A&M University

Harvey Greenwald
California Polytechnic State
University—San Luis Obispo
Mohammed Kazemi
University of North Carolina—
Charlotte
Dean Moore
Florida Community College at
Jacksonville

xx

PREFACE

James Olsen
North Dakota State University

Giovanni Viglino
Ramapo College of New Jersey

Virginia Puckett
Miami Dade College

Hiroko K. Warshauer
Texas State University—San Marcos

Mary E. Rerick
University of North Dakota

Jennifer Whitfield
Texas A&M University

Anne Siswanto
East Los Angeles College
I also thank those previous edition reviewers whose comments and suggestions have
helped to get the book this far.
Daniel D. Anderson
University of Iowa

David Gross

University of Connecticut

Randy Anderson
California State University—Fresno

Murli Gupta
George Washington University

Jim Bruening
Southeast Missouri State University

Kedrick Hartfield
Mercer University

Connie Carruthers
Scottsdale Community College

Karen J. Hay
Phoenix College

William J. Carsrud
Gonzaga University

Yvette Hester
Texas A&M University

Charles Clever
South Dakota State University

Xiaoming Huang

Heidelberg College

William Coppage
Wright State University

Jeff Knisley
East Tennessee State University

Margaret Crider
Tomball College

John Kutzke
University of Portland

Lyle Dixon
Kansas State University

Michael Lambe
Grossmont College

Bruce Edwards
University of Florida at Gainesville

Lowell Leake
University of Cincinnati

Charles S. Frady
Georgia State University

Richard J. O’Malley

University of Wisconsin—Milwaukee

Howard Frisinger
Colorado State University

Maurice Monahan
South Dakota State University

William Geeslin
University of New Hampshire

Richard Nadel
Florida International University

Larry Gerstein
University of California at Santa
Barbara

Karla V. Neal
Louisiana State University
Lloyd Olson
North Dakota State University