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tmua.me Medium Set C Paper 1 · Q17

Paper 1Functions & graphsAlgebra

For each real number aa, the curve CaC_a has equation

y=14x4−32x2+ax,0≤x≤3.y=\frac14x^4-\frac32x^2+ax,\qquad 0\leq x\leq3.

Let M(a)M(a) be the greatest absolute value of the gradient of CaC_a on this range of xx.

For which value of aa is M(a)M(a) as small as possible?

A−18-18
B−10-10
C−9-9
D−8-8
E00
F88

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