# 2018-02 Impossible to squeeze

For $$n\ge 1$$, let $$f(x)=x^n+\sum_{k=0}^{n-1} a_k x^k$$ be a polynomial with real coefficients. Prove that if $$f(x)>0$$ for all $$x\in [-2,2]$$, then $$f(x)\ge 4$$ for some $$x\in [-2,2]$$.

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