Problem #PRU-111264

Problems Calculus Functions of one variable. Continuity Continuity and compactness Monotonicity, boundedness

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?

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