The strategy for using derivative to prove inequality problem in college entrance examination mathematics
例析高考数学运用导数证明不等式问题的策略

摘要

导数背景下的不等式证明问题在高考命题中占据重要地位， 常常以选择题和解答题的形式出现. 新高考政策实施后，不等式导数问题的所占比重相比于旧高考有所提升. 此类试题灵活多变，通常设有两至三个小问，设计及类讨论、方程、化归等数学思想，在考察学生对知识技能的掌握程度的，还培养了学生的数学思维和推理能力。在实际教学中，我们发现部分学生面对导数背景下不等式的证明问题时束手无策，选择放弃，甚为可惜。本文以近年高考原题为例，归纳高考数学中常见的导数不等式问题并提供解决此类问题的常用策略，以此来帮助学生更好地分析并掌握解决该类题型的方法和技巧，从而提升解题效率。

Abstract

The problem of proving inequalities under the context of derivatives is of great importance in the college entrance examination, often appearing in the form of multiple-choice questions and solution problems. After the implementation of the new college entrance examination policy, the proportion of derivative-based inequality problems has increased compared to the old college entrance examination. Such questions are flexible and varied, usually with two to three sub-questions, and incorporate discussion, equation, and reduction to the basic form mathematical ideas. They not only test students' understanding of knowledge and skills, but also cultivate their mathematical thinking and reasoning ability. In actual teaching, we found that some students are at a loss when faced with the problem of proving inequalities under the context of derivatives and choose to give up, which is very regrettable. This article takes recent college entrance examination original questions as examples to summarize the common derivative inequality problems in college entrance examination mathematics and provide commonly used strategies for solving such problems. This is intended to help students better analyze and master the methods and skills for solving this type of problem, thereby improving their problem-solving efficiency.