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IMC 1998 Problem 8

Source: IMC 1998 Day 2 Problem 2

October 28, 2020
algebrapolynomialinequalities

Problem Statement

SS ist the set of all cubic polynomials ff with ∣f(±1)∣≤1|f(\pm 1)| \leq 1 and ∣f(±12)∣≤1|f(\pm \frac{1}{2})| \leq 1. Find sup⁡f∈Smax⁡−1≤x≤1∣f′′(x)∣\sup_{f \in S} \max_{-1 \leq x \leq 1} |f''(x)| and all members of ff which give equality.
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