Local minimum
This original textbook reading covers part of the AP topic. Follow the AP course outline for complete topic instruction and practice.
- Local minimum
Occurs when the derivative of a function is zero or undefined, and the surrounding values are higher than the value of the function at that point.
Examples:
- Related Glossary Terms
Absolute maximum, Absolute minimum, Critical points, Local maximum
- Index
Glossary and deeper reading · 1 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Local extremum
A local extremum is a value at least as large as, or at least as small as, all values at nearby allowed inputs. A local maximum compares nearby heights above, while a local minimum compares them below. For example, x² has a local minimum at 0. A local extremum need not be the greatest or least value over the entire domain.