tmua.me Tau Paper 1 · Question 17

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tmua.me Tau Paper 1 · Q17

Paper 1CalculusAlgebra

A polynomial $p$ has degree $6$ and leading coefficient $1$ . For every real $t$ ,

\int_{t-1}^{t+1}p(x)\,dx\geq0,

with equality if and only if $t=-2$ or $t=2$ .

Which one of the following describes all the possible values of $p(1)-p(0)$ ?

p(1)-p(0)<55

p(1)-p(0)<\dfrac{499}{9}

p(1)-p(0)\le27

p(1)-p(0)\le\dfrac{499}{9}

p(1)-p(0)\le55

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