MathDB

A1

Part of 1946 Putnam

Problems(1)

Putnam 1946 A1

Source: Putnam 1946

3/10/2022
Suppose that the function f(x)=ax2+bx+cf(x)=a x^2 +bx+c, where a,b,ca,b,c are real, satisfies the condition ∣f(x)∣≤1|f(x)|\leq 1 for ∣x∣≤1|x|\leq1. Prove that ∣f′(x)∣≤4|f'(x)|\leq 4 for ∣x∣≤1|x|\leq1.
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