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- Mar 10, 2012

- 835

I have no good ideas on how to go about solving the following:

Let $f:[a,b]\to\mathbb R$ and $g:[a,b]\to\mathbb R$ be real values functions both of which are differentiable in $(a,b)$. Show that there is an $x\in(a,b)$ such that $$\left(\frac{f(b)-f(a)}{b-a}\right)^2+\left(\frac{g(b)-g(a)}{b-a}\right)^2\leq (f'(x))^2+(g'(x))^2$$

Please help.