1, first find the first derivative, which is the first derivative (or first differential);

2. Let the first derivative function be 0, and the calculated x is called a static point;

3. Continue to derive the first derivative function and get the second derivative function.

Substitute the x of the static point into the second derivative function,

If it is greater than zero, the static point just now is the minimum point;

If it is less than zero, the static point just now is the maximum point;

If it is equal to zero, the static point just now is neither a maximum point nor a minimum point, which is called an inflection point.

Inflexion = POI = inflexion = concave inflection point on the image.

4. Substitute the coordinates of the static point into the original function to get the maximum or minimum value.

Description:

As upstairs said, draw a table and discuss it without calculating the second derivative.

This is a method, but it is not applicable. It is a teaching method with half the effort.

On the one hand, it is a waste of time; On the other hand, students are not given a complete concept and do not know the meaning and application of the second derivative.

It is not conducive to future study.

This method of drawing tables is understandable, but it is best to use it once or twice when solving problems. Usually get into the habit of calculating the second derivative.

The concept can be complete, the method is advanced, the time is saved, and it is beneficial to the study of subsequent courses.

No matter how the teacher renders the drawing method, he must keep a clear head in order to get twice the result with half the effort in future study!

Please call me if you have any questions.