TMUA 2017 Paper 1 Q10 — Worked Solution

P1·Differentiation·6.5Official · 2017 · Q10

parameter-optimisationnormal-gradientquadratic-in-parameter

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

M

. What is the greatest possible value of

M

p

varies?

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