Let $a,b\in \mathbb{R}$ with $a<b$, and let $f:[a,b]\to\mathbb{R}$. Suppose that $f$ has a local \reftext{def:local-extremum-at-point-1d-2026a}{extremum} at an interior point $c\in (a,b)$ and that $f$ is \reftext{def:derivative-interior-point-c54-2026b}{differentiable} at $c$. Then