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Putnam 1940 A2

Source: Putnam 1940

February 22, 2022
Putnamcalculusderivative

Problem Statement

Let A,BA,B be two fixed points on the curve y=f(x)y=f(x), ff is continuous with continuous derivative and the arc AB^\widehat{AB} is concave to the chord ABAB. If PP is a point on the arc AB^\widehat{AB} for which AP+PBAP+PB is maximal, prove that PAPA and PBPB are equally inclined to the tangent to the curve y=f(x)y=f(x) at PP.
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