# Math Genius: \$f:(a,+infty)rightarrowmathbb{R} \$ is differentiable function. I need explicit proof of a problem I find obvious

If $$f'(x)>c, forall xin(a,+infty)$$ where $$c>0$$. Prove that $$lim_{xto+infty} f(x) = +infty$$. I would say that this is trivial, how could we prove this explicitly?
$$f(x) = f(a) + int_a^x f'(t) , dt ge f(a) + c(x-a)$$