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DOI：http://dx.doi.org/10.26855/jamc.2022.09.010

# Methods and Skills of Solving Several Kinds of Differential Mean Value Theorem Proving Problems

Date: October 19,2022 |Hits: 229 Download PDF How to cite this paper

Lijuan Hou*, Guodong Shi

Taishan University, Tai’an, Shandong, 271000, China.

*Corresponding author: Lijuan Hou

### Abstract

The differential mean value theorem is one of the important basic theorems in differential calculus and a powerful tool to study the properties of the Han script. It reflects the relationship between functions and derivatives. Many proof questions encountered in the study of calculus need to use the relevant knowledge of the differential mean value theorem, and students are often at a loss. In this paper, several types of differential mean value theorems are discussed in depth, and it is found that the key point and difficulty in proving many propositions related to differential mean value theorems is to construct appropriate auxiliary functions. By constructing auxiliary functions, abstract and seemingly unrelated conclusions can be transformed into relatively straightforward views, which can easily find the path that meets the conditions of differential mean value theorems, and then solve the problem. Through these types of questions, this paper summarizes the common skills to find auxiliary functions, hoping to provide some help for students in learning, postgraduate entrance examination, etc.

### References

[1] Chen Wendeng. Core questions of Mathematics for postgraduate entrance examination (Science and Engineering Mathematics I) [M]. Beijing: Beijing University of Aeronautics and Astronautics Press, 2009.

[2] Chen Wendeng, Huang Xiankai, Zhu Qingyu. Guide to Review Mathematics for Postgraduate Entrance Examination in 2020 (Mathematics II) [M]. Beijing: China Financial and Economic Publishing House, 2019.

[3] Li Xiaojuan. Exercises related to solving differential mean value theorem by skillfully constructing auxiliary functions [J]. Education and Teaching Forum, 2017 (40): 223-224.

[4] Wang Jiaying. Research on Problem Solving Strategies for Several Types of Differential Mean Value Theorem Questions [J]. Research on Advanced Mathematics, 2020, 23 (05): 13-14+17.

[5] Chen Yijia, BaiLiyan. The Application of Analogy in Mathematical Analysis [J]. Journal of Yuxi Normal University, 2015, 31 (08): 29-34.

### How to cite this paper

Methods and Skills of Solving Several Kinds of Differential Mean Value Theorem Proving Problems

How to cite this paper:  Lijuan Hou, Guodong Shi. (2022) Methods and Skills of Solving Several Kinds of Differential Mean Value Theorem Proving Problems. Journal of Applied Mathematics and Computation6(3), 375-379.

DOI: http://dx.doi.org/10.26855/jamc.2022.09.010