Official papers

Official 2017 Paper 1 · Q10

Paper 1Algebra

A curve CC has equation y=f(x)y=f(x) where

f(x)=p3−6p2x+3px2−x3f(x)=p^3-6p^2x+3px^2-x^3

and pp is real.

The gradient of the normal to the curve CC at the point where x=−1x=-1 is MM.

What is the greatest possible value of MM as pp varies?

A−32-\frac32
B−23-\frac23
C−12-\frac12
D14\frac14
E23\frac23
F32\frac32

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