Prove: if $\displaystyle f(x)$ is differentiable on the open interval $\displaystyle (a,b)$ and $\displaystyle \lim_{x\to a+}f(x) = \lim_{x\to b-}f(x)$ then there exists $\displaystyle c$ in the interval such that $\displaystyle f'(c)=0$.

It's almost clear that I need to use Rolle's theorem, but how do I overcome the fact that the given $\displaystyle (a,b)$ is an open interval?