MathDB

Let

f:\;\mathbb{R}\to\mathbb{R}

be a continuously differentiable function that satisfies

f'(t)>f(f(t))

for all

t\in\mathbb{R}

. Prove that

f(f(f(t)))\le0

for all

t\ge0

.
Proposed by Tomáš Bárta, Charles University, Prague.

Problem Statement