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?
A $- \frac { 3 } { 2 }$
B $- \frac { 2 } { 3 }$
C $- \frac { 1 } { 2 }$
D $\frac { 1 } { 4 }$
E $\frac { 2 } { 3 }$
F $\frac { 3 } { 2 }$
& E
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?

A $- \frac { 3 } { 2 }$

B $- \frac { 2 } { 3 }$

C $- \frac { 1 } { 2 }$

D $\frac { 1 } { 4 }$

E $\frac { 2 } { 3 }$

F $\frac { 3 } { 2 }$