Hi, I am stuck on this question.

Prove

$\displaystyle |f(L)-f(0)|^2 \le L \int_0^L |f'(x)|^2 dx$ for any function $\displaystyle f \in C^1([0,L])$.

So I know I should use the Cauchy-Schwarz inequality applied to the functions f′ and 1, but I am stuck on how to do it.

Thanks for any help people.