Prove or disprove.
If $f: \mathbb{R} \rightarrow \mathbb{R}$ is a differentiable function, $f'(x) > f(x)$ for all $x$, and $f(0) = 0$, then $f(x) > 0$ for all $x>0$.
If I could be pointed in the right direction, it would be highly appreciated.
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