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Question Number 125621 by ZiYangLee last updated on 12/Dec/20

$$\mathrm{Consider}\mathrm{a}\mathrm{continuously}\mathrm{differentiable}$$$$\mathrm{function}f:[0,1]\to \mathbb{R}\mathrm{such}\mathrm{that}f\left(0\right)=0$$$$\mathrm{and}f\left(1\right)=1.\mathrm{Find}\mathrm{the}\mathrm{minimum}$$$$\mathrm{value}\mathrm{of}{\int }_0^1{\left(f^{\prime }\left(x\right)\right)}^2\sqrt{1+x^2}dx$$

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