Topic summary
Local maximum
Extracted from the Wikipedia article Maximum and minimum.
Definition
In both the global and local cases, the concept of a strict extremum can be defined. For example, x is a strict global maximum point if for all x in X with x ≠ x, we have f(x) > f(x), and x is a strict local maximum point if there exists some ε > 0 such that, for all x in X within distance ε of x with x ≠ x, we have f(x) > f(x). Note that a point is a strict global maximum point if and only if it is the unique global maximum point, and similarly for minimum points.