A Study On The Maximum And Minimum Value Problem In High School Mathematics

The maximum and minimum value problem occupies an important position in high school mathematics,which is not only one of the key examination contents of mathematics in college entrance examination,but also an important foundation of optimization problem in real life.Because relevant knowledge is comprehensive,complex,flexible,abstract,a lot of students often can not find the entry point in the problem solving,their solutions are not so comprehensive,when meeting this kind of problem in the exam,they will have the mood-fear of difficulty.The purpose of this thesis is to systematically classify the main types of maximum and minimum value problems and study the general methods to solve them,so as to provide help students to achieve better learning results.Viewed from the point of concept courses,recitation courses and revision courses,this paper puts forward with the strategy of teaching design,which can provide reference for teachers.This paper mainly shows the following five aspects of research: firstly,through the teacher interview,students are tested survey to analyze whether students have mastered the knowledge of the maximum and minimum value problem in a certain degree,and find out the main problems that students have when solving this kind of mathematical problems.Secondly,by analyzing the distribution of the maximum and minimum value problem in the textbook and establishing the classification basis of the maximum and minimum value problem,they are capable of sorting out the knowledge related to the maximum and minimum value(including the method of finding the conditional extreme value by Lagrange multiplier method in advanced mathematics).Thirdly,I analyzed the maximum and minimum value problem showed in the last five years of national college entrance examination papers,and summed up the main examination points,the types of questions and the main mathematical ideas and methods contained in the exams.Fourthly,the main types and corresponding solutions of the maximum and minimum value problem are determined by the three aspects above.The main types are as follows :(1)the maximum and minimum valueproblem in the functions(quadratic function,trigonometric function,high-order function,fractional function without square root,function with square root,exponential function and logarithm function,inequality invariance problem,problem of finding parameter value range,double maximum value problem,practical application of function maximum value);(2)The maximum and minimum value problem in sequence(find the maximum and minimum terms,find the maximum and minimum value of the preceding sum and the constancy in the arithmetic sequence);(3)the maximum and minimum value problem in analytic geometry(using geometry to find the maximum and minimum value and using algebra to find the maximum and minimum value);(4)the maximum and minimum value problem in inequalities(linear programming,fundamental inequality,absolute value inequality,Cauchy inequality).Fifthly,put forward with the strategy of teaching design and give three teaching designs of concept lesson,recitation lesson and review lesson.