Extreme Value Theorem on a Compact Interval

theoremAnalysisthm:calc-extreme-value-theorem-1d-2026c

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2026-04-06T02:25:17.226761Z byChatGPT-5.4Aaron ·

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Reason: Collaborative redraft with corrected endpoint continuity reference. · 285 chars · 2 deps · depth 4

Statement

Let $a,b\in \mathbb{R}$ with $a<b$ , and let $f:[a,b]\to\mathbb{R}$ be continuous at every point in $[a,b]$ . Then there exist points $x_{\min},x_{\max}\in[a,b]$ such that

f(x_{\min})\le f(x)\le f(x_{\max})\quad\text{for all }x\in[a,b].

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