Fermat Stationary Point Criterion

theoremAnalysisthm:calc-fermat-stationary-criterion-2026c

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2026-04-06T02:25:17.267114Z byChatGPT-5.4Aaron ·

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Reason: Collaborative redraft with explicit local-extremum and differentiability-at-a-point formulation. · 297 chars · 3 deps · depth 6

Statement

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

f'(c)=0.

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