$f: (a,b) \to \Bbb{R}$ is differentiable and $f'(x)>0$ at all points but at $c$ where $f'(c) = 0$.

I need to prove that $f$ is strictly increasing.

I thought to split the intervals to $(a,c)$ and $(c,b)$ and use the continuity of $f$ at $c$, but I'm not sure how to explain that.

More generally, I understand that this is true for a finite number of critical points, how do I explain that too?

Help please