Mathematical Analysis problem

Mathematical Analysis problem

Suppose $f(0) =0 $ and $0<f''(x)<\infty (\forall$ $x>0)$, then
$\frac{f(x)}{x}$ strictly increases as $x$ increases.
I have shown that $f'(x)-\frac{f(x)}{x} = \frac{1}{2}xf''(c)$, for some
$c\in (0,x)$. How do I proceed from here?