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Putnam 1959 A7

Source: Putnam 1959

June 15, 2022
Putnamfunctioncalculusderivative

Problem Statement

If ff is a real-valued function of one real variable which has a continuous derivative on the closed interval [a,b][a,b] and for which there is no x∈[a,b]x\in [a,b] such that f(x)=f′(x)=0f(x)=f'(x)=0, then prove that there is a function gg with continuous first derivative on [a,b][a,b] such that fg′−f′gfg'-f'g is positive on [a,b].[a,b].
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