If it is greater than (less than) the function values of other points in the neighborhood, it is a strict maximum (less than). This point is correspondingly called extreme point or strict extreme point.
Extreme value is a basic concept of variational method. The maximum or minimum value obtained by a functional within a certain allowable function range is called the maximum or minimum value respectively, and is collectively called the extreme value. The radial angle function that makes the functional reach the extreme value is called the extreme value function. If it is a univariate function, it is usually called an extreme curve. Extreme value is also called relative extreme value or local extreme value.
Extreme value is a general term for "maximum value" and "minimum value". If the value of a function at a certain point is greater than or equal to the value of any other point near that point, the value of the function at that point is called the "maximum value" of the function. If the value of a function at a certain point is less than or equal to the value of any point near that point, the value of the function at that point is called the "minimum value" of the function.
The relative maximum or relative minimum reached by a function in some local areas of its domain. When the value of a function at a certain point in its definition domain is greater than the value of any point around that point, the function is said to have a maximum at that point; When the value of a point in the definition domain of a function is less than the value of any point around that point, the function is said to have a minimum value at that point.