Home > Olympiad > IMC 2012 Problem 4

IMC 2012 Problem 4


Let {f: \Bbb{R} \rightarrow \Bbb{R}} be a continuously differentiable function that satisfies {f'(t)>f(f(t))} for all {t \in \Bbb{R}}. Prove that {f(f(f(t))) \leq 0} for all {t \geq 0}.

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