SIMON-MARAIS 2025 A1

A function $f: [0, \infty) \to [0, \infty)$ is max-poly if there exist finitely many polynomials with real coefficients $p_1(x), p_2(x), \ldots, p_n(x)$ such that

• $p_i(x) \geq 0$ for all $x \geq 0$ and $1 \leq i \leq n$, and
• $f(x) = \max(p_1(x), p_2(x), \ldots, p_n(x))$ for all $x \geq 0$.

Determine whether the function $f(x) = \min(x, x^2)$ is max-poly.