Problem

In this question you must show all stages of your working.

Solutions relying on calculator technology are not acceptable.

A curve has equation

$$16x^3-9kx^2y+8y^3=875$$

where $k$ is a constant.

(a) Show that

$$\frac{dy}{dx}=\frac{6kxy-16x^2}{8y^2-3kx^2}$$

Given that the curve has a turning point at $x=\dfrac52$

(b) find the value of $k$