摘  要：微分中值定理不仅是微分学的基本定理，而且它也是微分学的理论核心。微积分的许多命题和不等式的证明都以它为依据, 在证明有关中值问题中具有极其重要的作用。可以讲，学好微分中值定理，能为进一步学好微积分理论打下坚实的理论基础。但我们在学习时却感到比较困难，本文通过证明中值定理、辅助函数的引入、证明不等式、函数最值，凸性与拐点等。并对微分中值定理加以应用和推广。

关 键 词：微分中值定理  辅助函数 证明  应用  推广

这个也太专业了,搞不定

是啊，如果这样专业的翻译，可能必须要专业翻译才行，坛子里的多是业余的

试译如下：

Introduction: The differential Mean Value Theorem (MVT) is not only the essential theorem of the differential, but also the core theory of the differential. Many propositions and proving of inequalities in calculus rely on MVT. MVT has been playing a very important role in the proving of mean value problems. Therefore, understanding MVT will make more solid theory foundation for studying calculus. We find that it is not quite easy to understand it. In this paper, we have proved MVT, introduced the auxiliary function, proved inequality, the maximum / minimum of a function, convexity, inflection points, etc., and found out the applications of MVT and extended its applications.

Key Words: Differential Mean Value Theorem, Auxiliary Function, Proving, Application, Extended

另，我不觉得“证明”，“应用”和“推广”三词应列为关键词。为尊重原文，还是译了。

呵呵，楼主可以借助下网站吧，好专业阿

Abstract: differential value theorem is not only derivative of the fundamental theorem, but it is also the theory of differential core. Calculus of many propositions and inequality have to prove that it is based on the proven value of the relevant issues in an extremely important role. Can speak, learn differential value theorem, for further study calculus theory lay a solid theoretical basis. But when we are learning more difficult, the paper by proving that value theorem, the introduction of auxiliary functions that inequality, the value function, such as convex and inflection point. And the differential in value theorem to application and promotion.

Key words: differential value theorem auxiliary function that promote the application of

另外，从我写paper的习惯和认识来看，还是不把 证明  应用  推广 放到关键词里比较妥当

引用:

原帖由 SH002 于 2008-5-29 17:38 发表
试译如下：

Introduction: The differential Mean Value Theorem (MVT) is not only the essential theorem of the differential, but also the core theory of the differential.

“of the differential”在上句中用了两次，可否只用一次？

谢谢指正。第一个“of the differential”可略去。