Extreme value is the maximum or minimum value of a function. If a function has a value everywhere in the neighborhood of a point, and the value of that point is the maximum (minimum), then the value of this function at that point is the maximum (minimum). 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.
Generally speaking, the maximum value of a function is divided into the minimum value and the maximum value. Simply put, the minimum value is the minimum value of the function in the definition domain, and the maximum value is the maximum value of the function in the definition domain. The geometric meaning of the maximum (minimum) value of a function-the ordinate of the highest (low) point of the function image is the maximum (minimum) value of the function.
Function definition:
Function, mathematical terminology. Its definition is usually divided into traditional definition and modern definition. The essence of these two functional definitions is the same, but the starting point of narrative concept is different. The traditional definition is from the perspective of movement change, and the modern definition is from the perspective of set and mapping.
The modern definition of a function is to give a number set A, assume that the element in it is X, apply the corresponding rule F to the element X in A, and record it as f(x) to get another number set B, assume that the element in B is Y, and the equivalent relationship between Y and X can be expressed as y=f(x). The concept of a function includes three elements: the domain A, the domain B and the corresponding rule F, among which the core is the corresponding rule F, which is the essential feature of the function relationship.