Let $f(x)$ be diffrentiable at $(a,b)$ for $a,b\in \mathbb{R}$. given that $f'(x)\neq 0$ for any $x\in (a,b)$ proove that $f(x)=0$ for not more than one point in $(a,b)$
Well, If I was given that $f(x)$ is also continus at $[a,b]$ I could easly show that with a contradiction to rolle's theorem.
Is it possible to show that without the given about the continuity? or there is a mistake in the question?