On the extremum of derivative The book says, "generally, the steps to find the maximum and minimum values of the function y = f (x) on [a, B} are as follows: 1. Find the extremum of function y = f (x) in (a, b); 2. Compare the extremum of function y = f (x) with the function values f (a) and f (b) at the breakpoint, where the largest one is the maximum and the smallest one is the minimum Question: is the extremum mentioned in 1 f '(x) = 0? Is the derivative value of the extremum point necessarily 0? Is it not the upper minimum and maximum value collectively referred to as extremum? Then the extremum has been found in 1, is it not the maximum and minimum value? Why should we calculate the second step?

On the extremum of derivative The book says, "generally, the steps to find the maximum and minimum values of the function y = f (x) on [a, B} are as follows: 1. Find the extremum of function y = f (x) in (a, b); 2. Compare the extremum of function y = f (x) with the function values f (a) and f (b) at the breakpoint, where the largest one is the maximum and the smallest one is the minimum Question: is the extremum mentioned in 1 f '(x) = 0? Is the derivative value of the extremum point necessarily 0? Is it not the upper minimum and maximum value collectively referred to as extremum? Then the extremum has been found in 1, is it not the maximum and minimum value? Why should we calculate the second step?

Extremum is the maximum or minimum value of a function in a local area (in the neighborhood of a point). Extremum is used to describe the behavior of a function in a local area. However, the maximum and minimum values are used to describe the behavior of a function in a whole area

Derivative extremum problem
Let f (x) be significant in (a, b) and have only two extremum in (a, b), then the larger value must be the maximum
Is this a true proposition? If so, is it possible to save the table? Please give me your advice
Well If it is a larger value, it must be a maximum value. Wrong number

True proposition
F (x) is significant in (a, b), and f (a), f (b) do not exist, so if there are only two extremum, the larger value must be the maximum

derivatives
1) For the problem of extremum, we have obtained the derivative of the function, but the derivative y 'is a first-order function, and X has only one root after y' = 0. How can we determine the extremum~
2) And how to find monotone interval when derivative y '= 4

(1) Method 1: after y '= 0, the root of X is the possible extremum point of the function, which is used to divide the domain interval of the function into two parts, and judge the monotonicity of the function in the two small areas respectively. If the monotonicity is opposite, then the point is the extremum point (left increase, right decrease, maximum; left decrease, right increase, minimum)
Method 2: find the second derivative of the function, and then take the root of X after y '= 0 into the expression of the second derivative. If the result is less than 0, then take the maximum value; if the result is less than 0, then take the maximum value
(2) When the derivative y '= 4, then y' > 0 is constant, so the function is monotonically increasing in the whole domain