Extreme Value Theorem
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.
Example
is continuous on the interval [−1, 4].
