Problem #PRU-111264

Problemas Cálculo Funciones de una variable. Continuidad Continuidad y compactación Monotonía, acotación

Problem

A continuous function \(f(x)\) is such that for all real \(x\) the following inequality holds: \(f(x^2) - (f (x))^2 \geq 1/4\). Is it true that the function \(f(x)\) necessarily has an extreme point?