Okay, I know I've seen this somewhere, but cannot prove it:

Given $\displaystyle f:[a,b]\rightarrow\mathbb{R}$ is continuous and nonnegative. Show that

$\displaystyle \lim_{n\rightarrow\infty}\left[\int_a^b (f(x))^n \; dx \right]^{1/n}=\mbox{max }\{f(x):x\in[a,b]\}$

All help would be greatly appreciated! Thanks!