Give the answer in terms of 32.
Trang 1Created by T Madas
Created by T Madas
Question 34
A curve C has equation
y= x − x +a , x∈ , where a is a constant
The tangent to C at the point where x = and the normal to C at the point where 2 1
x = , meet at the point Q
Given that Q lies on the x axis, determine in any order …
a) … the value of a
b) … the coordinates of Q
8 3
a= , ( )7 ,0
3
Q
Trang 2Created by T Madas
Created by T Madas
Question 35
The curve C has equation
3
x x x y
x
−
= , x∈ , x> 0
a) Determine expressions for dy
dx,
2 2
d y
dx and
3 3
d y
dx
b) Show that the y coordinate of the stationary point of C is −k34, where k is
a positive integer
c) Evaluate d y22
dx at the stationary point of C
Give the answer in terms of 32
d) Find the value of d y33
dx at the point on C , where
2
2 0
d y
dx =
MP1-M , 3 32
dy
2
2
2 60 480
d y
3
3 120 240
d y
dx
−
3072
k= , 960 2 , 360 3