微分法证明不等式摘要 不等式是解决问题的工具，也与许多的数学知识相联系，因此，不等式的证明也尤为重要. 在高中试题与数学分析试题中就存在许多的不等式的证明，而证明往往与其他的知识联系在一起，因此难度就被增加了.对近五年有关不等式证明的高中与数学分析中的试题进行研究分析，得到微分法证明的几种方法.微分法是最基础的证明方法. 分析函数单调性；拉格朗日定理；凹凸性；柯西中值定理；最大值最小值；泰勒公式在证明不等式中的应用.归纳总结运用微分法证明不等式的几种方法的一般步骤. 运用这几种证明不等式的微分方法，使得证明变得简单，便于学生理解与学习不等式，思路明晰. 建议使用合适的微分方法来证明不等式，简化证明过程，解决数学问题.关键词 微分法 不等式 导数Proving Inequality by Differential MethodAbstract Inequality is a tool to solve mathematical problems. Therefore, the proof of inequality is particularly important. High school mathematical questions and mathematical analysis test about proving inequalities in the near years are researched and analysed, Several methods about proving Inequality by Differential Method are obtained, Utilizing function monotonicity, lagrange median theorem, concave and convexity of function,cauchy mean value theorem and maximum and minimum of function are analysed and discussed in inequality. Datum and literature about proof of inequality are consulted and analysed. Many methods of proving inequality are received. Inequality is proved by many differential methods, and these methods aren’t difficult. Inequality are proved quickly by differential methods, proof of inequality are analysed. Constructing auxiliary function are needed. Then, properties of auxiliary function are used. General steps in several approaches about proving inequalities by differential method are induced and summarized. Easy for students to understand and learn. Differential methods about proving Inequalities are becomed simp...
