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f' (0) <= A, quadratic , | f(x)| <= 1 for 0 <= x <= 1

Source: Polish MO Finals 1970 p6

August 22, 2024
quadraticsalgebrainequalities

Problem Statement

Find the smallest real number AA such that, for every quadratic polynomial f(x)f(x) satisfying ∣f(x)∣≤1 | f(x)| \le 1 for 0≤x≤10 \le x \le 1, it holds that f′(0)≤Af' (0) \le A.
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