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IMC 2005 day 2 pb 4

Source: Peter

July 26, 2005
calculusderivativegeometrytrapezoidintegrationrectangleIMC

Problem Statement

Let f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} be a three times differentiable function. Prove that there exists w∈[−1,1]w \in [-1,1] such that f′′′(w)6=f(1)2−f(−1)2−f′(0). \frac{f'''(w)}{6} = \frac{f(1)}{2}-\frac{f(-1)}{2}-f'(0).
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