Given a differentiable function $f: (0,\infty) \rightarrow \mathbb R $ and $c>0$ such that $f'(x)>c$ for every $x$.
Prove: $\lim _{ x\rightarrow\infty }{ f(x) }=\infty$
Using the MVT, I got to $f(x)>c(x-x_0)+f(x_0)$, and I think I should proceed using the definition of limit, but I got stuck.
Any help appreciated.