TMUA 2017 · Paper 1 · Question 10

A curve $C$ has equation $y = f (x)$ where

f (x) = p^{3} - 6 p^{2} x + 3 p x^{2} - x^{3}

and $p$ is real.

The gradient of the normal to the curve $C$ at the point where $x = - 1$ is $M$ .

What is the greatest possible value of $M$ as $p$ varies?