Find the derivative f' (x);

Find the root of equation f'(x)=0;

Check the sign of the left and right f'(x) values in the equation. If Zuo Zheng is negative to the right, then f(x) gets the maximum at this root; If the left is negative and the right is positive, then f(x) takes the minimum value at this root.

F'(x) Meaningless points should also be discussed. You can first find the root of f'(x)=0 and the meaningless point of f'(x), and then judge according to the definition.

2. To find the extreme point:

Find the x value of f' (x) = 0 and f "(x) ≠ 0;

This paper discusses the discontinuous point of f(x) with the definition of extreme value (the point where the value of f(x) is less than or greater than this point in the neighborhood of infinitesimal radius is the extreme point).

The set of all the above points is the set of extreme points.

Extended data:

Definition:

If the function f(x) is in x? Definition of a neighborhood d, x division? All points of have f (x)

Similarly, if all points of d have f (x) >; f(x？ ), just call f(x? ) is the minimum value of the function f(x).

The concept of extreme value comes from the problem of maximum and minimum value in mathematical application. According to the law of extremum, every continuous function defined in a bounded closed region must reach its maximum and minimum. The problem is to determine at which point it reaches the maximum or minimum.

If the extreme point is not a boundary point, then it must be an interior point. Therefore, the first task here is to find a necessary condition for an interior point to become an extreme point.

References:

Baidu Encyclopedia-Ultimate Value