Let \( \mathrm{f} \) defined on \( [0,1] \) be a twice differentiab...

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Let \( \mathrm{f} \) defined on \( [0,1] \) be a twice differentiable function such that, \( \left|\mathrm{f}^{\prime \prime}(\mathrm{x})\right| \leq 1 \) for all \( \mathrm{x} \in[0,1] \) If \( \mathrm{f}(0)=\mathrm{f}(1) \), then show that, \( \left|\mathrm{f}^{\prime}(\mathrm{x})\right|1 \) for all \( x \in[0,1] \)
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