MathDB
Putnam 1999 B4

Source:

December 22, 2012
Putnamfunctioncalculusderivativelimitcollege contests

Problem Statement

Let ff be a real function with a continuous third derivative such that f(x)f(x), f′(x)f^\prime(x), f′′(x)f^{\prime\prime}(x), f′′′(x)f^{\prime\prime\prime}(x) are positive for all xx. Suppose that f′′′(x)≤f(x)f^{\prime\prime\prime}(x)\leq f(x) for all xx. Show that f′(x)<2f(x)f^\prime(x)<2f(x) for all xx.
Back to ProblemsView on AoPS