For a function of one variable
Then, we say that is a critical point for if either the derivative equals zero or is not differentiable at (i.e., the derivative does not exist).
Note that the term critical point is not used for points at the boundary of the domain.
The value is termed the critical value.
The term critical point is also sometimes used for the corresponding point in the graph of .
For a function of multiple variables
For further information, refer: critical point for function of multiple variables
- Point of local extremum implies critical point: If a function attains a local extreme value (local maximum or local minimum) at a point in the interior of its domain, then that point must be a critical point.