关于函数的凸性在中学数学解题中的应用摘 要 近年来，关于凸函数的这一知识点的考察已经可以在各地的模考卷甚至是高考卷中不断找到踪迹，稍微复杂一点的高中数学题都有可能存在凸函数的考察点。但是，纵观主流高中数学教材，对于凸函数的详细介绍却鲜有提及。在实际应用中，用凸函数的应用思维来启迪学生找到更加行而有效的解题办法是至关重要的，这也能大大帮助现在的高中生提高数形结合的能力。比较常见的是一些题目涉及到了三角不等式的概念，对它进行计算或者证明，初见这种题目有时可能不知所措，但是仔细研究这类题的本质，就会发现凸函数起到了至关重要的作用，加以利用就能使得答题过程更加简洁明了，同样在对数函数和指数函数的题目中也能找到凸函数的身影。本文通过对一些结构复杂繁琐的不等式的证明，应用凸函数的基本模型解释以及经典的性质，大大简化了证明过程。通过这些定义和性质，也更能让学生自发的去理解求取值范围、最值这类题目，从而可以提高学生的系统性解题能力和对知识的全面掌控。这也更加能够证明凸性函数在高中数学题目中至关重要的内容。关键词 上（下）凸函数 单调性 不等式On the application of convexity of function in middle school mathematics problem solvingAbstract In recent years, the investigation of this knowledge point about the convex function has been able to find traces in the model test papers and even the college entrance examination papers everywhere. It is possible for the slightly more complicated high school mathematics questions to have the investigation point of the convex function. However, looking at mainstream high school mathematics textbooks, there is little mention of the detailed introduction to convex functions. In practical applications, it is crucial to use the thinking of convex function to enlighten students to find more practical and effective problem-solving methods, which can also greatly help current high school students to improve their ability to combine numbers and shapes. It is more common that some problems involve the concept of triang...
