MathDB

Putnam 1946 A4

Source: Putnam 1946

March 13, 2022

Putnamfunctioncalculusderivative

Problem Statement

Let

g(x)

be a function that has a continuous first derivative

g'(x)

. Suppose that

g(0)=0

and

|g'(x)| \leq |g(x)|

for all values of

x.

Prove that

g(x)

vanishes identically.