Solution
= Solution
If $f$ is continuous on $[a,b]$, <differentiable> on $(a,b)$, and $f(a)=f(b)$, then some $c\in(a,b)$ has $f\prime(c)=0$. A maximum or minimum is attained; unless $f$ is constant, one extremum lies inside, where the <derivative> vanishes.