The point with stagnation point f'(x)=0 is the extreme point; The derivative of the original function at x=0 is not 0, and it is not a stagnation point. Therefore, the extreme point is not necessarily the stagnation point, and the stagnation point is not necessarily the extreme point. The extreme point can be derivative or non-derivative. The derivative case of extreme point is stagnation point, and the non-derivative case can be sharp point or corner point. According to the concept of stagnation point, as long as the first derivative is 0, it does not mean that it must be an 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.

In calculus, stagnation point is also called stagnation point, stable point or critical point. The first derivative of the function is zero, that is, at this time, the output value of the function stops increasing or decreasing. For the image of one-dimensional function, the tangent of the stagnation point is parallel to the X axis. For the image of two-dimensional function, the tangent plane of the stagnation point is parallel to the xy plane.