If a function f(x) is continuous on the closed interval [a, b], then f(x) has an abosolute maximum and minimum on the interval [a, b].

That is, there exist numbers x1 and x2 in [a,b] such that:

The extreme value theorem does not indicate the value of the maximum and the minimum values, it only determines if they exist.


is continuous on the interval [−1, 4].

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