The extreme point is the abscissa of the maximum or minimum point in the subinterval of the function image.

The extremum point appears at the stagnation point (the point where the derivative is 0) or the non-derivative point of the function (the derivative function does not exist, so the extremum can be found, and the stagnation point does not exist at this time).

If f(a) is the maximum or minimum value of the function f(x), then a is the extreme point of the function f(x), and the maximum and minimum points are collectively called extreme points. The extreme point is the abscissa of the maximum or minimum point in the subinterval of the function image. The extremum point appears at the stagnation point (the point where the derivative is 0) or the non-derivative point of the function (the derivative function does not exist, so the extremum can be found, and the stagnation point does not exist at this time).

Second, the definition and proof of logarithmic mean

(Logarithmic mean inequality can't be directly used in college entrance examination, so it needs to be proved in solving problems. )