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:

Extreme Value Theorem

Extreme Value Theorem

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

Example

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

Extreme Value Theorem

Extreme Value Theorem