关于函数的凸性在中学数学解题中的应用

On the application of convexity of function in middle school mathematics problemsolvingAbstract In recent years,the investigation of this knowledge point about the convex function hasbeen able to find traces in the model test papers and even the college entrance examination paperseverywhere.It is possible for the slightly more complicated high school mathematics questions to havethe investigation point of the convex function.However,looking at mainstream high schoolmathematics textbooks,there is little mention of the detailed introduction to convex functions.Inpractical applications,it is crucial to use the thinking of convex function to enlighten students to findmore practical and effective problem-solving methods,which can also greatly help current high schoolstudents to improve their ability to combine numbers and shapes.It is more common that someproblems involve the concept of triangular inequalities.Calculate or prove it At first sight,suchproblems may sometimes be overwhelming,but if you carefully study the nature of such problems,youwill find that the convex function plays a vital role.The role of the function can be used to make theanswering process more concise and clear,and the figure of the convex function can also be found inthe problems of the logarithmic function and the exponential function.This paper greatly simplifies theproof process by proving some complex and cumbersome inequalities,applying the basic modelinterpretation of convex functions,and classical properties.Through these definitions and properties,students can also spontaneously understand such questions as the range of values and the maximumvalue,which can improve students'ability to solve problems systematically and control theirknowledge.This also proves that the convexity function plays a vital role in high school mathproblems.Key words Convex function monotonicity inequality