The curve goes through the point $P(4, 3)$ and satisfies $\frac{dy}{dx} = \frac{8}{x^2} - \frac{10}{(2x - 3)^2}$.
(a)[3]
Find the equation of the normal to the curve at $P$. Present your answer in the form $y = mx + c$.
(b)[3]
Find the rate of change of the gradient of the curve at $x = 4$.
(c)[5]
The curve is also known to pass through the point $(-1, q)$. Find the value of $q$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substituting $4$ gives the curve gradient as $\frac1{10}$” …