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Here is the question: Let $f(x)$ be a three times differentiable function on $[−1, 1]$ such that $f(−1) = 0$, $f(0) = 0$, $f(1) = 1$ and $f′(0) = 0$. Prove that $f′′′(x) ≥ 3$ for some $x ∈ (−1, 1)$.
My attempt: Well I think I have to use either the mean-value theorem or Taylor's Theorem, or both. I have no idea. Can someone just give a hint in order for me to start on this problem? Thank you very much!!