AP Calculus AB and BC glossary
Extremum
Also called: Maximum, Minimum, Extreme value
An extremum is a maximum or minimum value of a function. A local extremum is largest or smallest compared only to nearby points, while an absolute extremum is largest or smallest across the entire domain or interval under consideration.
Local extrema occur only at critical points. Absolute extrema on a closed interval occur either at a critical point or at an endpoint, which is why the candidates test checks both.
The distinction between the location and the value is worth guarding. The extremum is the output value; the point where it happens is the coordinate. Questions ask for one or the other and rarely both.
Endpoints
An endpoint can hold an absolute extremum but never a local one under the usual convention, because a local extremum needs points on both sides to compare against.
Appears in: Unit 5: Analytical Applications