According to the derivative of the function, the specific methods for judging the maximum and minimum are as follows:

[1] Let the function y=f[x], then y'=f'[x].

[2] When making an image of y'=f'[x], every intersection with the X axis is the extreme point of y=f[x].

[3] As for the maximum or minimum, it can be judged according to whether the "needle threading" is bottom-up (minimum) or top-down (maximum).

Refer to Figure 1:

In addition, the "thread method" is also applied in junior high school mathematics, such as:

Add x 3-2x 2-x+2 >: 0 to (x-2)(x- 1)(x+ 1) >; 0

The roots of (x-2)(x- 1)(x+ 1)=0 are: x 1 = 2, x2 = 1, x3 =- 1.

Refer to Figure 2:

Note: Needle-piercing method, also known as "multi-axis root-piercing method" or "using several axes method"