What is the extreme point of 1. function? For the function y=f(x), if all functions except x0 are greater than (less than) f(x0) in the neighborhood of a point x0 within its definition domain, then x=x0 is called a minimum (maximum) value point of the function, and f(x0) is called a minimum (maximum) value point of the function; 2. What is the stagnation point of a function? The function y=f(x) is continuously differentiable in the interval a, so if f'(x0)=0, x0 is called the stagnation point of y=f(x). Stationary point is the solution that makes the derivative equal to 0. 3. Relationship between extreme point and stagnation point: (1) function y=f(x) is continuously derivable. If x=x0 is the extreme point of the function, then f'(x0)=0. That is to say, "x=x0 is the extreme point of the function" means "f'(x0)=0. For example: f (x) = x 3. Then f'(x)=0 and x=0, but x=0 is not an extreme point; On the premise that the function is differentiable, some stagnation points are extreme points and some are not. Only when the signs of the derivative values on the left and right sides of the stagnation point are opposite, the stagnation point must be an extreme point, otherwise it is not an extreme point. (2) If the function doesn't know whether it is differentiable, it doesn't matter. For example, y=|x| is nondifferentiable at x=0, but x=0 is a minimal point.