导数在不等式证明中的应用导数知识是高等数学中极其重要的部分,它的内容,思想和应用贯穿于整个高等数学的教学之中.利用导数证明不等式是一种行之有效的好方法,它能使不等式的证明化难为易,迎刃而解.在不等式证明的种种方法中,它占有重要的一席之地.本文将从利用函数的单调性,利用函数的最值, 利用泰勒公式，利用微分中值定理,利用函数的凹凸性及利用两导数的不等性等六个方面阐述导数在不等式证明中的应用.
关键词：证明 导数 不等式 函数
The apply of derivative in prove inequality
Abstract：The knowledge of derivative is an extremely important part of higher mathematic，its content ,ideas, and applications impenetrate into the teaching of higher mathematic. As to the proofs of inequalities, the use of the derivative proved to be an effective measure. It earns a place in the various methods of the proofs of inequalities. This article will elaborate the application of derivative in the use of the proofs of inequalities, that is, the monotonic property of the function, the maximum or minimum value of a function, differential mean value theorem, Taylor’s formula, concavity, inequality of two derivative.
Key words: evidence derivative inequalities function
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