Convex Function?Jensen Inequality And Its Application In Middle School Mathematics

Convex function is a kind of important function, for study of concave and convex functions, in the various branches of mathematics have great usefulness. Convex function itself has many excellent properties, and these properties in many areas of mathematics have widely used, especially in the college entrance examination and mathematics competition is very important application, it involves the many mathematical propositions and theoretical proof and applications.Firstly, this paper simply introduces the convex function of several equivalent definitions and properties of judgment and Jensen inequality proof, deformation and promotion; secondly, elaborated the convex function and Jensen inequality in middle school teaching reflects the educational value and function; finally, the convex function and Jensen inequality in high school mathematics application system, comprehensive, clear division. For example:for the similar questions are given a unified method of solving problems is to simplify the proving process, and develop the students' problem-solving ideas. For some questions, and gave the corresponding promotion, such as the solution circle inscribed and circumscribed polygon of the most value problem "promotion" for solving elliptic Inscribed, circumscribed polygons of most value problem ". After the system, comprehensive, clear arrangement, for the students to this part of the knowledge involved in relevant questions have more in-depth understanding, learn to use convex function nature and piano students inequality can be more convenient and simple solution must related issues, also for students to provide some new ideas and problem-solving skills.