Extreme Value Theorem

Definition

The Extreme Value Theorem states that if a function is continuous on a closed interval, then it must have both a maximum value and a minimum value on that interval.

Related terms

Critical Points:

These are points on a function where the derivative is either zero or undefined.

Absolute Extrema:

These are the highest and lowest values of a function over its entire domain.

Closed Interval Method: This method involves evaluating the function at its critical points and endpoints to find local extrema.