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Bài tập CALCULUS 14
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Created by T. Madas
Question 55
(***)
y
C
O
P
x
The figure above shows the cubic curve C which meets the coordinates axes at the
origin O and at the point P .
The gradient function of C is given by
f ′ ( x ) = 3x 2 − 8 x + 4 .
a) Find an equation for C .
b) Determine the coordinates of P .
C1H , f ( x ) = x3 − 4 x 2 + 4 x , P ( 2,0 )
Created by T. Madas
Created by T. Madas
Question 56
(***)
The point P ( 8,18) lies on the curve C , whose gradient function is given by
dy
= 8 3 x − 10 , x ≥ 0 .
dx
Find an equation for C .
4
C1L , y = 6 x 3 − 10 x + 2
Question 57
(***)
A curve C has equation given by
y=
1 + 3x3
x2
, x≠0
Find the coordinates of the point on C where the gradient is 1.
(1, 4 )
Created by T. Madas
Created by T. Madas
Question 58 (***)
The temperature, T in °C , of a hot drink t minutes after it was made is given by
1
T = 90 − 8t + t 2 , 0 ≤ t ≤ 8 .
2
a) Calculate after how many minutes the drink has a temperature of 60 °C .
b) Find the rate of change of temperature of the drink 4 minutes after it was made.
t = 6 , −4 °C / min
Question 59
(***)
Show clearly that
4
3
3 x−
4
dx = k 3 ,
x
where k is an integer to be found.
k =2
Created by T. Madas
