Bài tập CALCULUS 77

Created by T. Madas
Question 259

(****+)

A quadratic curve C passes through the points P ( a, b ) and Q ( 2a, 2b ) , where a and
b are constants.

The gradient at any given point on C is given by

dy
= 2x − 6 .
dx
Find an equation for C , in terms of a .

C1Y , y = x 2 − 6 x + 2a 2

Created by T. Madas


Created by T. Madas
Question 260

(****+)

A curve has equation

y = 2 x3 +

k
− 19 ,

x

x>0,

where k is a positive constant.
If the y coordinate of the stationary point of this curve is 45 , find the value of k .
SYN-Q , k = 96

Created by T. Madas


Created by T. Madas
Question 261

(****+)

y
y=

x2 + 6
x4

9
4

O

k

x

2k

The figure above shows the graph of the curve with equation

y=

x2 + 6
x4

, x>0.

The area of the region between the curve and the x axis for k ≤ x ≤ 2k , where k is a
positive constant, is exactly 9 .
4

a) Show clearly that
9k 3 − 2k 2 − 7 = 0 .

b) Hence find the value of k , showing further that there is no other value of k
which satisfies the equation of part (b).
C2V , k = 1

Created by T. Madas