中值等式问题证明的方法探究

Exploration of Methods for Proving Median Equality Problems

文章以历届全国研究生入学考试高等数学考题及历届全国大学数学竞赛真题(含某些省市的竞赛试题)为例,对中值等式问题的证明作了比较详尽的分析.得出结论:在中值等式问题的证明中,一般需要构造辅助函数,而辅助函数的构造可以用间接积分的方法得到,而且此方法坡度小、难度低,学生容易掌握.

The paper provides a detailed analysis of the proof of the median equality problem by taking the advanced mathematics exam questions of previous national postgraduate entrance exams and the real questions of previous national university mathematics competitions(including competition questions of certain provinces,cities and universities) as examples.It is pointed out that in the proof of median equality problems,auxiliary functions are generally constructed,and the construction of auxiliary functions can be completely obtained by the method of indirect integration,which has the advantages of small slope and low difficulty,and it is easy for students to master.