7.4: The Supremum and the Extreme Value Theorem
https://math.libretexts.org/Bookshelves/Analysis/Real_Analysis_(Boman_and_Rogers)/07%3A_Intermediate_and_Extreme_Values/7.04%3A_The_Supremum_and_the_Extreme_Value_Theorem
WebMay 28, 2023 · Theorem \(\PageIndex{2}\): Extreme Value Theorem (EVT) Suppose \(f\) is continuous on \([a,b]\). Then there exists \(c\), \(d ∈ [a,b]\) such that \(f(d) ≤ f(x) ≤ f(c)\), for all \(x ∈ [a,b]\). Sketch of Proof. We will first show that \(f\) attains its maximum.
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