导数对函数性质的逻辑判断

摘 要： 2000年开始的新课程试卷命题中有关导数的内容其考试要求都是很基本的，随年逐渐加深，其重点考查的内容是导数的概念和计算，以及导数函数应用问题，不过多地涉及理论探讨和严格的逻辑证明。本文首先阐述了导数的概念，及导数的意义。其次是导数的简单应用，包括导数与函数图像之间的关系及运用导数求函数的极值、单调区间、证明函数的增减性等。再次是用导数解决三次函数，这类问题是近年高中理科试卷中经常涉及到的，也是近年来的一个热点问题。最后是综合考查，包括解决应用问题，将导数内容和传统内容中有关不等式和函数的单调性等有机地结合在一起，设计综合题，通过将新课程内容和传统内容相结合，加强了能力考察力度，使试题具有更广泛的实际意义，更体现了导数作为工具分析和解决一些函数性质问题的方法，这类问题用传统教材是无法解决的。
关键词：导数；函数；单调性；
Derivative function of the nature of the logic of judgement
Abstract：In 2000 started in the new curriculum examination paper proposition the related derivative's content its test request was very basic, deepened gradually along with the year, its key examination's content was the derivative concept and the computation, as well as the derivative function application question, not excessively many involved the theory discussion and the strict logical proof. This article first elaborated the derivative concept, and derivative significance. Next is the derivative simple application, asks the function including between the derivative and the function image's relations and using the derivative the extreme value, the monotony interval, the certificate function fluctuation and so on. Is with once more derivative solution cubic, this kind of question was in the recent years high school science subjects examination paper involves frequently, was also a recent years's hot topic. Finally synthesizes the examination, including the solution application question, in the derivative content and the traditional content the related inequality and the function monotonous and so on organically unifies in together, the design synthesis synthesis, through unifies the new curriculum content and the traditional content, strengthened ability inspection dynamics, enables the test question to have a more widespread practical significance, manifested the derivative to analyze and to solve some function nature question method as the tool, this kind of question used the traditional teaching material is the inextricability
Keywords ：Derivative；Function ；Monotony；

目　　录

1导数应用的题型与方法.....................................................................................................2
1.1导数的定义...................................................................................................................2
1.2导数的几何意义...........................................................................................................3
2导数与函数图像之间的关系.............................................................................................3
3用导数研究函数的性质......................................................................................................3
3.1导数研究函数的单调性......................................................... ......................................3
3.2导数求函数极值............................................................................................................5
3.3导数解决生活中函数问题............................................................................................6
4导数解决三次函数..............................................................................................................7
5导数的注意事项.................................................................................................................8
6 范例分析............................................................................................................................9
参考文献..............................................................................................................................16
致谢......................................................................................................................................17