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Chisinau MO p180 1979 X trinomial, |f '(0) | <= 8 if |f(x) | <=1 for0<x<=1

Source:

March 17, 2021
trinomialalgebraderivative

Problem Statement

It is known that for 0≤x≤10\le x \le 1 the square trinomial f(x)f (x) satisfies the condition ∣f(x)∣≤1|f(x) | \le 1. Show that ∣f′(0)∣≤8.| f '(0) | \le 8.
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