Definition: A function value $z(c,d)$ is a minimum of the function $z(x,y)$ if for each $(x,y)$ in the neighborhood of $(c,d)$, $$\[ z(x,y)\geq z(c,d). \]$$ The point $(c,d)$ is called a minimum location of the function $z(x,y)$.
A function value $z(c,d)$ is a maximum of the function $z(x,y)$ if for each $(x,y)$ in the neighborhood of $(c,d)$, $$\[ z(x,y)\leq z(c,d). \]$$ The point $(c,d)$ is called a maximum location of the function $z(x,y)$.
Remark 1: An extremum is either a minimum or a maximum.
Remark 2: An extremum is defined locally.
Remark 3: An extremum on the boundary of the domain is called a boundary extremum.
Remark 4: Minimum and maximum are defined non-strictly. (See Monotonicity.)
A function value $z(c,d)$ is a maximum of the function $z(x,y)$ if for each $(x,y)$ in the neighborhood of $(c,d)$, $$\[ z(x,y)\leq z(c,d). \]$$ The point $(c,d)$ is called a maximum location of the function $z(x,y)$.
Remark 1: An extremum is either a minimum or a maximum.
Remark 2: An extremum is defined locally.
Remark 3: An extremum on the boundary of the domain is called a boundary extremum.
Remark 4: Minimum and maximum are defined non-strictly. (See Monotonicity.)