AP Calculus AB and BC glossary

Absolute extremum

Also called: Global extremum

An absolute extremum is the single highest or lowest value a function reaches on an interval. On a closed interval you find it with the Candidates Test: evaluate the function at every critical point and at both endpoints, then compare the numbers.

The Extreme Value Theorem is what guarantees these exist. It needs a continuous function on a closed interval, and without both hypotheses the maximum can simply fail to be attained.

The mistake

Forgetting the endpoints. An absolute extremum on a closed interval frequently occurs at an endpoint, where the derivative says nothing at all.

Appears in: Unit 5: Analytical Applications