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数学分析中有几个微分中值定理:罗尔中值定理、拉格朗日中值定理,柯西中值定理都是微分学中十分重要的定理,对微分学影响巨大,而它们的证明正是以构造辅助函数为桥梁,才得以完成。数学本来就是贯通的,所以这种构造辅助函数的方法在中学数学解题中也发挥着重要的作用。下面笔者会用一些例子来说明怎样去构造一个具体的函数,又怎样利用函数的性质去解决具体问题。
There are several differential mean value theorems in mathematical analysis: the Rolle median value theorem, Lagrange median value theorem and Cauchy median value theorem are all very important theorems in differential calculus, which have great influence on differential calculus, and their proofs are exactly To construct the auxiliary function as a bridge, to be completed. Math has always been through, so this method of constructing auxiliary functions also plays an important role in solving mathematical problems in high schools. Below I will use some examples to illustrate how to construct a specific function, how to use the nature of the function to solve specific problems.