3.35: Quotient/product derivative and stationary points

0606/12/M/J/24 — Question 8 · 8 marks

A curve has equation

y = \dfrac{(4x + 2)^{\frac{1}{2}}}{(3x - 5)^{2}}

(a)

Show that

\dfrac{\mathrm{d}y}{\mathrm{d}x}

can be written as

\dfrac{Ax^{2} + Bx + C}{(3x - 5)^{2}(4x + 2)^{\frac{1}{2}}}

, where

A

B

and

C

are integers.

[5]

(b)

Hence find the

x

-coordinates of the stationary points on the curve, in simplest exact form.

[3]