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IMC 2016, Problem 7

Source: IMC 2016

July 28, 2016
IMCIMC 2016college contestsfunctionminimum value

Problem Statement

Today, Ivan the Confessor prefers continuous functions f:[0,1]→Rf:[0,1]\to\mathbb{R} satisfying f(x)+f(y)≥∣x−y∣f(x)+f(y)\geq |x-y| for all pairs x,y∈[0,1]x,y\in [0,1]. Find the minimum of ∫01f\int_0^1 f over all preferred functions.
(Proposed by Fedor Petrov, St. Petersburg State University)
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