I have been struggling with this problem..
Q. Let $f(x)$, $x\geq 0$, be a non-negative continuous function, and let $F(x)=\int_0^x f(t) dt$, $x\geq0$. If for some $c>0$, $f(x)\leq cF(x)$ for all $x\geq 0$, then show that $f(x)=0$ for all $x\geq0$ .
I have tried everything in my ability, but in vain. I get a feeling that this can be solved using Mean Value theorem. Any ideas? Please help!!