AP Calculus AB and BC glossary

Relative extremum

Also called: Local extremum

A relative extremum is a point that is highest or lowest compared only with nearby points. It occurs at a critical point where the first derivative changes sign, and it need not be the largest or smallest value the function takes overall.

The sign change is what matters, not the derivative being zero. A function can have a zero derivative with no extremum, as x cubed does at the origin, because the slope never changes sign.

The mistake

Reporting the x-value when the question asks for the maximum value. The location is an x-coordinate; the value is the corresponding output.

Appears in: Unit 5: Analytical Applications