Function Monotonicity And Its Application In High School Mathematics

Function and its monotonicity is an extremely important part of the current high school mathematics teaching material contents, especially the monotonicity. It is the important foundation of knowledge for student learning series, analytic geometry, inequality and so on. But for the monotonicity of function, the resources of its systematic proved methods and its applications to solve problems, are limited, which leads to a lot of difficults for a glimmer of teachers’ teaching senior high school and senior high school students in learning monotonicity, for example:students can’t properly choose which method to prove monotonicityFor this problem, this paper arranges like this.The first chapter puts forward the problem to study, and then summarizes the relevant research literatures, and it points out the thinking of writing the thesis.The second chapter gives the related conclusion of function monotonicity. Through comparison and analysis of three commonly used textbooks and reference of teachers in China about the definition of function monotonicity of narrative, on this basis, the convenience for the later research, this paper gives the new definition, which prepares for the following part of the theory.The third chapter summarizes the judgment methods of function monotonicity, namely the definition method, direct judgment method, equivalent definition method, the complex function method, derivative method; And the examples explain the solving model of these methods, and conditions of how to choose these methods.The fourth chapter systematically discusses the function monotonicity in the application of the high school mathematics. In this part, the thesis combines the Shaanxi province college entrance examination examination test in recent years.The relevant function monotonicity paper has been researched and analyzed. The application of the relevant function monotonicity is systematically summarized and listed, respectively using function monotonicity to determine the range of parameter selection, to solve equation, to prove inequality, to settle inequality, and solve practical problems.Conclusion part summarizes the main points of this paper, and points out the meaning of teaching practice.