Let $I$ be an interval in the sense of \ref{def:interval-real-line-c54-2026a}, let $[a,b]\subseteq I$ with $a<b$, and let $f:I\to\mathbb{R}$ be continuous on $[a,b]$ in the sense of \ref{def:continuity-closed-interval-c54-2026a} and differentiable at every point of $(a,b)$ in the sense of \ref{def:derivative-interior-point-c54-2026b}. Assume that $f(a)=f(b)$. Then there exists $c\in(a,b)$ such that