Investigation And Research On High School Students Using Derivatives To Solve Function Extremum Problems

Function is an important main line in high school mathematics courses and one of the main contents of mathematics learning for high school students.Regarding the extreme value of function,the 2017 edition of "Curriculum Standards" proposed in the calculus part of two types of courses:Derivatives will be used to discuss the extremum of functions,and geometric figures will be used to illustrate the necessary and sufficient conditions for a point to be an extremum(no mathematical proof is required).However,many high school students have problems in solving the extremum of functions difficult.This study summarizes the types of difficulties that high school students use to derive function extremums,analyzes the difficulties that high school students have when solving function extremum problems,and gives coping strategies.In the study,the literature research method,test survey method and questionnaire survey method were used.First of all,through the test investigation,it can be seen that the sophomore students have difficulties in understanding the concept,formula operation,and knowledge transfer by using the derivative to solve the function extremum.Secondly,the results of the questionnaire survey indicate that the difficulty of understanding the concept of extremums in high school students is that the derivative content is more abstract and difficult to apply to the extremum content of the function;the difficulty in formula calculations is due to the inability to use the derivation rule or inexperience and The lack of thinking or ability of transformation and substitution of the function analytical formula;the reason for the difficulty in connecting the new and old knowledge is that the transfer of knowledge cannot be used flexibly,and it is related to the sequence,derivative,image and nature of the function,etc.When considering the problem Single thinking lacks flexibility.Finally,according to the various reasons why students have difficulty in using the derivative to find the extreme value of the function,this paper proposes the following three strategies:learn to pay attention to the understanding of the basic concepts of derivatives and extreme values,master the law.of differentiation;accurately analyze the discrete Continuous and flexible use of derivative methods to solve problems;master construction skills,overcome operational difficulties,and solve extreme point offset problems.