Let $f\left(x\right),x\ge 0$, be a non-negative continous function,and let $F\left(x\right)={\int }_0^{x}dt,x\ge 0$, if for some $c>0,f\left(x\right)\le cF\left(x\right)$ for all $x\ge 0$, then show that $f\left(x\right)=0$ for all $x\ge 0$.

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