Let's assume $r < a < b < t$ , and a function $f:[r,t] \to \mathbb{R}$ , $f $ differentiable in $(r,t)$, with $f'(a)< 0 < f'(b)$ . Prove that there exists $c$ such that $a<c<b$ and $f'(c) = 0$
(So basically, i want to something like Bolzano for $f'$, although $f'$ may not be continuous)
