I could use some help getting started on this proof. Any help would be appreciated.

Prove that if $\displaystyle f:[0,1]\rightarrow \mathbb{R}$ is differentiable and $\displaystyle f(0)=f(1)=0$, then for any $\displaystyle a\in \mathbb{R},\exists c\in (0,1)$ such that $\displaystyle f'(c)=af(c)$.

I was told a hint that I have to apply Rolle's Theorem to $\displaystyle f(x)e^{ax}$ but I'm not sure how to work that in yet...