$f(0)=0,\ f'(X)$ is str. increasing: prove that $f(X)/X$ is also increasing function all $X \in(0, \infty)$
Show that $x \mapsto \frac{f(x)}{x}$ is strictly increasing on (0,1) given that f '(x) is strictly increasing on (0,1) and that f(0)=0