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About. Transcript. The Extreme value theorem states that if a function is continuous on a closed interval [a,b], then the function must have a maximum and a minimum on the …

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Extreme Value Theorem. The Extreme Value Theorem (EVT) says: If a function f is continuous on the closed interval a ≤ x ≤ b, then f has a global minimum and a global maximum on that interval. In finding the optimal value of some function we look for a global minimum or maximum, depending on the problem. How do we know that one exists?

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