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), \[z(x,y)≥z(c,d).\] 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), \[z(x,y)≤z(c,d).\] 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), \[z(x,y)≤z(c,d).\] 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.)