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| f' (y)| = 4 \int _0^1 | f(x)|dx

Source: 1987 Swedish Mathematical Competition p4

March 28, 2021
integrationanalysisalgebra

Problem Statement

A differentiable function ff with f(0)=f(1)=0f(0) = f(1) = 0 is defined on the interval [0,1][0,1]. Prove that there exists a point y∈[0,1]y \in [0,1] such that ∣f′(y)∣=4∫01∣f(x)∣dx| f' (y)| = 4 \int _0^1 | f(x)|dx.
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