Help me please with this one, I think it's refers to Mean value theorem, but not sure...

Let us, derivative of a function$\displaystyle f(x)$ - is continuous and $\displaystyle f(0)=1$. Also $\displaystyle \forall x>0: f'(x)>f(x) $.

Prove that $\displaystyle \forall x>0: f(x)>e^{x}$

Thanks!