中值类等式证明中辅助函数的3种构造方法

Three constructing methods of auxiliary function in the proof of a median value equality

在中值定理的基础上,提出一类含有中值的等式证明过程中构造辅助函数的3种方法,即观察法、经验法和求解微分方程构造法,通过示例分析和比较分析,阐明3种方法的特点和适用情况.并将数学思维训练和数学素养培养贯穿始终,有助于培养学生逻辑思维能力,从而提高分析问题和解决问题的能力.同时,也为学生攻克专升本数学考试的证明专题提供一种有效途径.

On the basis of the median theorem, proposes three methods of constructing auxiliary function in the process of proving the equality of the mean which includes observation method, experience method and construction method for solving differential equations. Through the example analysis and comparative analysis, clarify the characteristics of three methods and application. The training of mathematical thinking and mathematical literacy throughout the training, help to cultivate students＇ logical thinking ability, and thus improve the ability to analyze and solve problems. At the same time, it provides an effective way for students to overcome the special topic of the mathematics examination.