Link full download test bank for applied calculus brief 6th edition by berresford

Test Bank for Applied Calculus Brief 6th
Edition by Berresford
Link full download: />
Chapter 2 Derivatives And Their Uses
1. Complete the table and use it to predict the limit, if it exists.
6x7
f ( x)

1

2

5 x

lim f (x) ?
x

x 0.5

f (x)

0.51
0.501
0.5001
0.5

?

0.4999
0.499
0.49

A) –160.0
B) 80.0
C) –80.0
D)
0.5
E) does not
exist Ans: C
2. Use properties of limits and algebraic methods to find the limit, if it exists.
3

lim (8x
x3

2

13x 3x 13)


A)

–121

B)

121

C)

141
D)

–141

E)

does not

exist Ans: B
3.
2
Find
lim x x without using a graphing calculator or
making tables. x 5 2 x 5
A)
2
B)
–5
C)
0
D)
4
E)
Ans: D

Berresford/Rockett, Brief Applied Calculus, 6e

4.
exists.
x 14

A)
B)

Use properties of limits and algebraic methods to find the limit, if it
–7 8x

lim

2
144x 5
9
14
1
14

1

C)

14
9

D)

14
E)
does not
exist Ans: D
5.
exists.

Use properties of limits and algebraic methods to find the limit, if it
2

lim x
x –5

92x 14

x

2x


A)

2
5

2
5

B)
C)

5
2
D)

5

2

E)
6.
exists.

does not

Use properties of limits and algebraic methods to find the limit, if it

lim 2x
x 13

exist Ans: B

2

4 x 32

x9 x 8

A)

17
12

B)

17
12

C)

12
17

12

D)

17
E)
does not
exist Ans: B

©2013 Cengage Learning. All Rights Reserved.
Page 38
Berresford/Rockett, Brief Applied Calculus, 6e

7.
Use properties of limits and algebraic methods to find the limit, if
it exists.
2

2

lim 9
9x
h0

h

A)

0

xh


B)
2x
C)
9x
D)
18x
E)
does not
exist Ans: D
8.
A graph of y f ( x) is shown and a c-value is given. For this
problem, use the graph to find lim f ( x) .
xc

c

2

A)
0
B)

2
C)
–6
D)
–4
E)
does not
exist Ans: A
9.
Use properties of limits and algebraic methods to find the limit, if
it exists.
16 7x
for x 3
lim f (x ), where f (x)
2

x3

A)

5

5xfor

x 3

C) –6

B) 6

D) –does not5
E)
exist Ans: E
10.
Find lim

x+6
f ( x) f ( x)
x–6 +

A)
B)
C)
D)
E)
Ans: D

6
–1
0
1
–6

.

for

x+6

©2013

Cengage Learning. All Rights Reserved.
Berresford/Rockett, Brief Applied Calculus, 6e

11.
Find lim f ( x) for the graph
of f ( x) given below. +
x

A)
B)
C)
D)
E)

3

0
-3
inf

3
Ans: A

12.
Find lim–

1.
x +1

x –1

B)
C)
D)
E)
F)
Ans: C

1
0
–1

13.
Find lim

–1

+

2

x 6

A)
B)
C)

6

D)

–6

.

x–6

0

E)
Ans: E

©2013 Cengage Learning. All Rights Reserved.
Page 40
Berresford/Rockett, Brief Applied Calculus, 6e

Page 39


14. For the given x-value, use the figure to determine whether the function is continuous or
discontinuous at that x-value.

x5
A)

discontinuous

continuous

B)
Ans: A
15. Determine whether the function is continuous or discontinuous at the given x-value.
2

x

if x –4

5

x –4

f (x )

9x

A)

123

if x –4

discontinuous

continuous
B)
Ans: B
16. Determine whether the given function is continuous. If it is not, identify where
discontinuous.

2
y 3x 4x 7
A)

discontinuous at x 5

B)

discontinuous at x 0

C)

discontinuous at x5

discontinuous at x 10 E)
D)
Ans: E

it is

continuous everywhere

17. Determine whether the function is continuous or discontinuous at the given x-value.
2
x
y
5
,x –7
x
4

A)

continuous

discontinuous
B)
Ans: A

©2013 Cengage Learning. All Rights Reserved.

Page 41


Berresford/Rockett, Brief Applied Calculus, 6e

18. Determine whether the given function is continuous. If it is not, identify where it
is discontinuous. You can verify your conclusions by graphing the function with a
graphing utility, if one is available.

y 8x 2 3x 7 x
12
A)

discontinuous at x

B)

discontinuous at x1

C)

discontinuous at x 1

D)

discontinuous at x1

1 2

2

continuous everywhere
E)
Ans: D

©2013
Page

Cengage Learning. All Rights Reserved.
42

Berresford/Rockett,
Applied Calculus, 6e

Brief

P,P,

and P ,

19.
slopes

By imagining tangent lines at points
state whether the

are
1
3

2

positive, zero,
or negative at these points.

A)

At P : positive slope
1

At P2 : negative slope
At P3 : positive slope
B)

At P : zero slope
1

At P2 : negative slope

At P3 : positive slope
C)

At P : zero slope


1

At P2 : positive slope
At P3 : negative slope
D)

At P : positive slope
1

At P2 : positive slope
At P3 : positive slope
E)

At P : positive slope
1

At P2 : negative slope
At P3 : negative slope
Ans: C

©2013 Cengage Learning. All Rights Reserved.

Page 43

20. Which graph represents f ( x) if the graph of f ( x) is displayed below?

A)

B)


Berresford/Rockett, Brief Applied Calculus, 6e

C)

D)

©2013 Cengage Learning. All Rights Reserved.

Page 44


Berresford/Rockett, Brief Applied Calculus, 6e

E)

Ans: C
21. For the given function, find the average rate of change over the specified
2
interval. f (x ) 5 5x 4x over
–2, 4
A)

0

B)

–19

C)

19

D)

13

–13
E)
Ans: E

22.
Find the average rate of change of f x
A)
B)
C)
D)
E)

8 x 7 between x

3 and x 8 .

8

7
3
11

5
Ans: A

23. Find the instantaneous rate of change of the function f x

2
6x 5x at x

2.


Berresford/Rockett, Brief Applied Calculus, 6e

A)

30

B)

26

C)

41

D)

42

E)

29

Ans: E

©2013 Cengage Learning. All Rights Reserved.

Page 45

24. For the function in this problem, find the instantaneous rate of change of the
function at the given value.
2
f (x ) 9x 5x 5; x 4
A)
0
B)
41
C)
31
D)
67
E)
77
Ans: D
25. For the function in this problem, find the slope of the tangent line at the
2 given

value. f (x ) 5x 9x 9; x 1
A)
1
B)
14
C)
–4
D)
0
E)
19
Ans: A
26. Find the slope of the tangent at x –1.
2
f (x ) 6x 2x
A)
–14
B)
–4
C)
–10
D)
4
E)
0
Ans: C


Berresford/Rockett, Brief Applied Calculus, 6e

27. For the function in this problem, find the derivative, by using
2 the
definition. f (x ) 5x 3x 9
A)
5 x 23 x 9
B)
5 x 2 3x
C)
10x
D)
5x 3
E)
10x 3
Ans: E
28. Find the slope of the tangent to the graph of f (x) at any
2
point. f (x) 9x 6x A)
18x 6
B)
18x 6
C)
9x 6
2
D)
9x
6x
E)
3x
Ans: A

©2013 Cengage Learning. All Rights Reserved.

29. Find f ' x
A)

Page 46

of f x –7 x 8 by using the definition of the derivative.

f ' x 8 B)
f ' x–7

C)
f ' x7x

D)

f ' x7

E)
f ' x –7 x

Ans: B
30. Write the equation of the line tangent to the graph of f (x) at x –1.
2
f (x) 5x 8x
A)
y –2 x 2
B)

y –2 x 2

C)

y –2 x


Berresford/Rockett, Brief Applied Calculus, 6e

D)

y –2 x 5

E)

y –2 x 5

Ans: D
2
31. The population of a town is f x
3 x 15 x 200 people after x weeks (for 0 x
). Find f ' x to find the instantaneous rate of change of the population after

20

8 weeks.
A)
48
B)

64

C)

33

D)

31

E)

49

Ans: C

32. An automobile dealership finds that the number of cars that it sells on day x of an 2
advertising campaign is S x x 18x (for 0 x 7 ). Find S ' x to find the
instantaneous rate of change on day x 2 .
A) 14
B) 18
C) 16
D) 22
E)
21
Ans: A

©2013 Cengage Learning. All Rights Reserved.

Page 47

Berresford/Rockett, Brief Applied Calculus, 6e

33. Differentiate the given function.

9x
y6

6
5

A)

6x

B)

9x

C)

9x

6
7
5

D)

54x

E)

9x

5

Ans: E

34.

4

Find the
derivative
of g w20 w .
A)
gw

5
4

3

w

3

4w
B)

4

20
4

g w

3

w

C)
gw
D)
g w 54 w3

E)
g w 20 4 w3
Ans: A
35. Find the derivative of the
1
2
function. y 5x 9x 13
A)
B)

–5 x 2 18x 3

3
–5 x 2 18x
1

C)

–5 18x
Page 48


D)

–5 x 2 9x 3

–5 x 1 9x 2
Ans: B
E)

36. For the function given, find f '(x).
4
f (x ) x
13x 8
3

x

13
3
B)
4x

8
3
C)
4x
13
4
D)
4x
13x
4
E)
x 13x 8
Ans: C
A)

©2013 Cengage Learning. All Rights Reserved.

Berresford/Rockett, Brief Applied Calculus, 6e

37. Find the derivative of the function.
10 / 3

8/3
30x 13 / 3

A)
B)
C)
D)
E)

–24 x 11/ 3

30x 7 / 3
30x 13 / 3

–24 x 5 / 3

f (x ) 9x
Ans: C
38.8

30x 7 / 3
–24 x 11/ 3

Find

–24 x 5 / 3

the
–72 x

derivative of f x
A)

fx

4

x.

2

3
4

B)

fx

2

x

9x
11/ 3

90x 13 / 3


C)

4 x5
f

x

4

3

1

D)
fx

2
49

E)

4x
fx

2
5
4 x

Ans: B
39. Find the derivative of the
4 2
function. y 7x 2x 6x 7
4
2
A)
28 x 4 x
6x7
3
B)
28 x 4 x

6
C)
7x3 2x
6
3
D)
28 x 4x

E)
7x4
Ans: B

2x2

6x 7

40. Find the derivative of the function.
21
11
8
h(x ) 11x 19x 7x 14x 6
20
10
7
A)
220 x 190 x 49 x 14
21
11
8
B)

231x 209 x 56 x 14x
20
10
7
C)
11x
19 x
7 x 14
20
10
7
D)
231x 209 x 56 x 14
21
11
8
E)
220 x 190 x 49 x
14x Ans: D

Page 50


©2013 Cengage Learning. All Rights Reserved.

Page 49

Berresford/Rockett, Brief Applied Calculus, 6e
41.

Find the derivative of
6.

3

hx 3

2

x
3

x A)

x

1
4
B)

x

3
C)

1
3

2

hx

2

hx
2

3x

D)
2

hx

3

1

3
E)

x

hx
Ans: C

2

x

2

4
x
1
hx
2

x
2
3

x
2
2

x
2
2

3
x

42. At the indicated point, find the instantaneous rate of change of the
function.
2
R (x ) 17x 2x , x 3
A)
29
B)

52

C)

19

D)

21

E)

23

Ans: A


43.

If

4

972 ,

x3
4

f x 60 find

f

x

A) B) f 81 14
f 81 15

C)
f 81

D)

21

f 81 16

E)
f 81 26
Ans: D

44. Find the derivative at the given x-value with the appropriate
rule. y 8 24 x at x 9
A) –8
B) –64
C) 8
D) –4
E) 0
Ans: D

©2013 Cengage Learning. All Rights Reserved.

Page 52

81 .


dx

x 25

B) df
–2
dx

x

25

45. Iff xx5 ,

find
A)
–32
dx

C) df 10

df

x –2

B)
df
–192

dx
dx

x 25

x –2

C)
320

D)

df

df
–10
dx

dx

25
x –2

D)

df

–128

E)
dx

4
df 80

dx

x –2

Ans: E

46.

df

x –2

E)
dx

x

x 25

Ans: A

If f x

30
250

x

Berresford/Rockett, Brief
Applied Calculus, 6e df

.
dx

x –2

x,

find
df .
A)

df 2

dx x

25

47. Suppose the Marginal Cost Businesses can buy multiple licenses

for PowerZip data
23

x compression

software at a total cost of approximately C x 24xdollars for licenses. Find the
derivative of this cost function at x 64 .
C 64 8

Page 53


B)

C 644

C)

C 642

D)

E)

A)

C 64 12

C 64 6

Ans: B

©2013 Cengage Learning. All Rights Reserved.

Berresford/Rockett, Brief Applied Calculus, 6e

48. Suppose the number of people newly inflected on day t of a flu epidemic is
2
3
f t 13t t (for 0 t 13) . Find the instantaneous rate of change of
this number on
day 10.
A)
f 10 300
B)
f 10–27

C)
f 10–40

D)
f 10 230
E)
f 10 60
Ans: C

answer.
3

49. Find the derivative of f x
A)

f x 1 32

B)

f x

3

x

x2

3

6
3

32

x

x2
3

Page 54

C)

f x 6 64

x

2
3

D)

fx

x

2 64 3

x2

3

E)

x

fx

3

2

32

x

3

2
Ans: D

x

6 3 x 8 x 1 by using the Product Rule. Simplify
your

50.

ds
Find dt

A)

B)

C)

8.

if s

6t 8
9t 8
6t

8

t

6

6t 5
5
48t
48t

8 t3

24t 2
3t 2
5

24t 2

6t 5 3t 2
5
2
9t 8 48t 24t
Ans: E

D)

9t 8

E)

©2013 Cengage Learning. All Rights Reserved.
Berresford/Rockett, Brief Applied Calculus, 6e

51.
7 x7

Find the derivative, but do not
simplify your answer. y 7 x 7 3 x 3 9 x
3 x 5 8 x 8 9 x9 6 A)
3x3

9 x 15 x 4 64 x 7 81x 849 x 6

9x2

93x5 8x8

9 x9

6

B)
15 x 4 64 x 7

81x 849 x 6

9 x2

9

C)
49 x 6 9 x 2

9 15 x 4

64 x 7 81x8

49 x 6 9 x 2

93x5 8x8

D)
9x9

67 x 7

3x3

9 x 15 x 4

64 x 7

81x8

E)

7x7

3x3

9 x 15 x 4

64 x 7 81x 849 x 6

9x2

93x5

8x8

9 x9

6


Ans: A

52.
15

z 28 z 14 1

Find the derivative of f z
Simplify your answer.
A)
f z43z 42 z

B)

f z42 z 43

29z 30

C)

f z42z 43

z

D)

f z43 z 42 30 z29 1

E)

f z43 z42

z

z by using the Product Rule.

z2

2

1

Ans: E

53.
Find the derivative of
A)

1

B)

6x
6

1
x 6

.

5

x7
C)

1
6x
D)

6x
5

E)
6 x Ans:

1
7

B

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Page 53

Page 56


Berresford/Rockett, Brief Applied Calculus, 6e

54. Find the indicated derivative and simplify.
x
7 3

C ( x) for C ( x)

4

7

2x

A)

14 x 2 2 x4

21

2

2 x4 7
B)
x 2 2 x4

21

2

2 x4

7

C)
x 2 2 x4

21

2

2 x4

7

D)

7 x 2 2 x4

21

2

2 x4

7

E)
7 x 2 2 x4

21

2

2 x4

7

Ans: D
55.
x5
4 x2

Find the derivative of f x

B)

5 by using Quotient Rule. Simplify your answer.

2

f x4 x

40 x 5

3

4 x2 5

A)

12 x 40 x 5 f x
2

5

f x4 x 2

40 x 5

2
3

4 x2

C)