In the college entrance examination in recent ten years, the discussion of functions and derivatives tends to be routine, and the investigation methods tend to be basic. However, in recent years, the characteristics of college entrance examination questions have changed, and more candidates are allowed to use derivatives as a tool to study functions. Derivative is like a ruler in a tailor's hand, which measures what the function in the stem looks like, thus making a series of analysis on the stem.

In senior high school, the study of derivatives can be divided into the following aspects:

1. derivative test standard questions for college entrance examination:

(1) characterization function;

(2) the connection with tangent in geometry (the tangent of plane curve can be studied by derivative method);

(3) The application of polynomial derivative is a difficult type.

2. There are many problems about the maximum value of function characteristics, so it is necessary to discuss them specially. The derivative method is faster and simpler than the elementary method.

3. The mixed problem of derivative and analytic geometry or function image.

4. For the stems of derivatives, we should learn to discuss them in categories. Most of them consider the image trend (such as slope and opening), the number of zeros (such as discriminant), the size of zeros (such as who is the biggest and who is the smallest), and whether the root is within the definition domain.

Knowledge integration of derivatives;

1. Understanding of the concept of derivative. The formula must be memorized, which is as important as Gai Lou's foundation! Don't memorize formulas by rote, but master how to apply formulas, why to use this formula and why to use other people's formulas. As for the derivation process, there will be special research in college mathematics, so there is no need to be too reluctant.

2. The method of judging the extreme value of differentiable function by derivative and finding the maximum and minimum value of some practical problems. The derivation rule of compound function is the key and difficult content in calculus. In the textbook, the law of derivative of compound function is introduced through examples, and then the law is proved.

3. In order to export correctly, you must do the following two things:

(1) Be familiar with the derivative formula of basic elementary functions, the derivative rules of sum, difference, product and quotient, and the derivative rules of compound functions.

(2) For a composite function, it is necessary to clarify the intermediate composite relationship and find out which variable should be derived from each decomposition function.

The study of derivative is equivalent to the stepping stone to the study of function. If the mathematical derivation is not thorough enough, it will affect the learning of the following functions ~