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> Let $f$ be an differentiable function. Show that $$\int\_{a}^{b} |f|^2\le\frac{(b-a)^2}{2}\int\_{a}^{b} |f'|^2$$
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Can you give me any Hint please (why not, $(b-a)^2$, where does the $\frac{1}{2}$ come from ?)