Problem

A curve passes through the point $P(4,3)$ and is such that

$\frac{dy}{dx}=\frac{8}{x^2}-\frac{10}{(2x-3)^2}.$

(a) Find the equation of the normal to the curve at $P$. Give your answer in the form $y=mx+c$.

(b) Find the rate of change of the gradient of the curve when $x=4$.

(c) Given that the curve also passes through the point $(-1,q)$, find the value of $q$.