MathDB

e^(f'(xi))*f(0)^(f(xi)) = f(1)^(f(xi))

Source: 26th annual VJIMC (2016), Category I, Problem 1

April 10, 2016

functionreal analysis

Problem Statement

Let

f: \mathbb{R} \to (0, \infty)

be a continuously differentiable function. Prove that there exists

\xi \in (0,1)

such that

e^{f'(\xi)} \cdot f(0)^{f(\xi)} = f(1)^{f(\xi)}