Let $a,b\in \mathbb{R}$ with $a<b$, and let $f:[a,b]\to\mathbb{R}$ be \reftext{def:continuous-at-point-c54-2026b}{continuous} at every point in $[a,b]$ and \reftext{def:derivative-interior-point-c54-2026b}{differentiable} at every point in $(a,b)$. Assume that $f(a)=f(b)$. Then there exists $c\in(a,b)$ such that