Solution
= Solution
<Rolle's theorem> states that, if $f$ is <continuous> on $[a,b]$, <differentiable> on $(a,b)$, $a<b$, and $f(a)=f(b)$, then
$$
\boxed{\text{there exists }\xi\in(a,b)\text{ with }f'(\xi)=0.}
$$
The endpoint equality and both regularity hypotheses are part of the assertion.