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A6

Part of 1980 Putnam

Problems(1)

Putnam 1980 A6

Source: Putnam 1980

4/1/2022
Let CC be the class of all real valued continuously differentiable functions ff on the interval [0,1][0,1] with f(0)=0f(0)=0 and f(1)=1.f(1)=1 . Determine the largest real number uu such that u≤∫01∣f′(x)−f(x)∣ dxu \leq \int_{0}^{1} |f'(x) -f(x) | \, dx for all ff in C.C.
Putnamfunctioncontinuous and differentiable