How to prove that function is 0?

Question

Let $f:[0,a]\to [0,\infty)$ be continuous function such that $f(0)=0$, $f'_+(0)=0$ and $f(x)\leq \int_0^x \frac{f(t)}{t}dt, \forall x\in [0,a]$. Prove that $f\equiv 0$. I don't have any idea how to deal with this. Any hint is welcome. Thanks in advance.