Minima and maxima

In mathematics, minima and maxima, known collectively as extrema, are the smallest value (minimum) or largest value (maximum), that a function takes in a point either within a given neighbourhood (local extremum) or on the whole function domain (global extremum).

Definition

Minimum

A real-valued function f is said to have a local minimum at the point x^*, if there exists some ε > 0, such that f(x^*) ≤ f(x) whenever |x − x^*| < ε. The value of the function at this point is called minimum of the function.

The definition of a local maximum is similar, only with the ≥ sign in place of ≤.

See also

• Extreme value