If the derivative is bigger than positive constant, is the limit at infinity infinity

Hello

I'm trying to prove the following: if $\displaystyle f$ is differentiable on all $\displaystyle R$ and there exists a real positive constant $\displaystyle c$ such that $\displaystyle f'(x)$ > c for all $\displaystyle x$, then the limit of f at infinity is infinity.

I've managed to prove that if the derivative is positive, then by the Mean Value Theorem the function must be strictly increasing. But I can't seem to manage to prove that the limit isn't some real number...