The point where the second derivative of the function is equal to 0 is called the inflection point, and it is also the point where the concavity and convexity of the function changes. Then you can choose the value of the second derivative, that is, the value in this inflection point interval to judge whether the second derivative is greater than 0 or less than 0. Greater than 0 is concave downward, less than 0 is convex upward. However, a point equal to 0 does not necessarily mean an extreme point.
The image inflection point of a function is the point where the second derivative is equal to 0, and the extreme point is also the point where the first derivative is equal to 0 and the second derivative is equal to 0, but they are not connected with each other, that is to say, there may be a point that is an inflection point, but it is not an extreme point. For example, it may happen that the lower part is convex and the upper part is concave, but its concavity has changed. The rising speed of this point has not changed, which is called inflection point, but it has changed.
The first derivative of the function is equal to 0, which is an extreme point, and then it may be the extreme point at the end point. However, in a limited interval, the extreme point and the inflection point are not a point, which can be inferred as an inflection point, not necessarily an extreme point, and the extreme point may be an inflection point, and there is no necessary connection between them.
The simplest and most effective way to judge the image of a function, such as the rise and concavity of its inflection point extreme point, is to find its first derivative and second derivative, and then draw its image. After the image is drawn, it is easy to judge whether it is an inflection point or an extreme point. It will be difficult to judge with something literal, and it goes without saying that neither inflection point nor extreme point is needed, that is to say, they may not affect each other, but they have both.