# Minimum/maximum

Definition:
• A function value $y(c)$ is a minimum of the function $y(x)$ if for each $x$ in the neighborhood of $c$ $y(x)\geq y(c).$ The point $c$ is called a minimum location of the function $y(x)$.
• A function value $y(c)$ is a maximum of the function $y(x)$ if for each $x$ in the neighborhood of $c$ $y(x)\leq y(c).$ The point $c$ is called a maximum location of the function $y(x)$.
Remark 1: An extremum is either a minimum or a maximum.

Remark 2: An extremum is locally defined.

Remark 3: An extremum at the boundary of the domain is called a boundary extremum.

Remark 4: Minimum en maximum are non-strictly defined. (See Monotonicity.)