Rolle's theorem

If $y=f(x)$ is:

1. continuous on a closed interval $[a,b]$
2. differentiable on open interval $(a,b)$
3. $f(a)=f(b)$

then there is at least one number, $c$, in $(a,b)$ at which $\frac{f(b)-f(a)}{b-a}=f^{\prime }(c)=0$