Let $f$ defined on $\left[0,1\right]$ be twice differentiable such that $\left|f\left(x\right)\right|\le 1$ for $x\in \left[0,1\right]$. if $f\left(0\right)=f\left(1\right)$ then show that $\mid f^{\prime }\left(x\right)<1$ for all $x\in \left[0,1\right]$.

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