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在函数类综合题中,对证明与函数有关的不等式、已知不等式在某范围内恒成立求参数的取值范围、讨论方程解的个数等类型的问题,我们常常需要构造辅助函数,通过求导研究其单调性或寻求其几何意义来解题.根据题目本身的特点,所构造的函数可有多种形式,导致解题过程的繁简程度不同.因此,正确分析函数不等式的结构,恰当构造函数成为解题的突破口.本文结合例题,向考生展示如何构
In the function class synthesis problem, we often need to construct helper functions to prove that the inequalities and known inequalities related to the function are constant within a certain range and the range of the parameters is discussed. Dictation studies its monotonicity or seeks its geometric meaning to solve the problem. According to the characteristics of the topic itself, the constructed function can take many forms, leading to different degrees of complexity in the problem-solving process. Therefore, the structure of function inequalities is correctly analyzed. Appropriate constructor functions as a breakthrough point for problem solving. This article combines examples to show candidates how to structure