Extreme Value Theorem

AP Calculus · Axiom Academy

Guaranteeing max and min values on closed intervals If a function is continuous on a closed interval , it must attain both a maximum and minimum value somewhere on that interval. This seems obvious, but it's actually a powerful theorem that depends on continuity! Extreme Value Theorem (Formal) At critical points (where = 0 or undefined) Finding Absolute Extrema: The Algorithm Find all critical points in (a, b) Evaluate the function at: Each critical point Compare values. The largest is the absolute max, the smallest is the absolute min.

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