Definition of extreme point
The concept of extreme value comes from the problem of maximum and minimum value in mathematical application. The maximum and minimum values of a function are collectively referred to as the extremum of the function, and the point where the function obtains the extremum is called the extremum point. Every continuous function defined on a bounded closed region is bound to reach its maximum and minimum. The problem is to determine at which point it reaches the maximum or minimum. If it is not a boundary point, it must be an interior point, then this interior point must be an extreme point. The first task here is to find a necessary condition for an interior point to become an extreme point. Let the function f(x) have a definition near X. If it is correct for X. Its centripetal neighborhood has f (x): f (x.), then f (x.) is a minimum value of the function f (x.) and the corresponding extreme point is X.