tmua.me Extreme Set A Paper 1 · Question 9

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tmua.me Extreme Set A Paper 1 · Q9

Paper 1CalculusAlgebra

A cubic polynomial $f(x)$ has coefficient $1$ for $x^3$ and satisfies

\int_0^1 f(x)\,\mathrm{d}x= \int_1^2 f(x)\,\mathrm{d}x= \int_2^3 f(x)\,\mathrm{d}x=0.

What is the greatest possible value of

\int_t^{t+1} f(x)\,\mathrm{d}x

as $t$ varies with $0\le t\le2$ ?

0

\dfrac{\sqrt3}{9}

\dfrac38

\dfrac{25}{64}

\dfrac{2\sqrt3}{9}

\dfrac{\sqrt3}{3}

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