Critical points
This original textbook reading covers part of the AP topic. Follow the AP course outline for complete topic instruction and practice.
- Critical points
Points on a graph within a specific interval that occur when the derivative is zero, is undefined, and at the edges of the interval. These are the points where the local/absolute maxima/minima occur.
- Related Glossary Terms
Absolute maximum, Absolute minimum, Local maximum, Local minimum
- 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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Critical point
A critical number is an input in the function’s domain where its derivative is zero or does not exist. The corresponding point on the graph is called a critical point. For example, x³ has a critical number at 0, but it has no local maximum or minimum there. Critical numbers are candidates for extrema and need further analysis; inputs outside the domain are excluded.