近五年全国三卷高考试题中导数问题的研究

近五年全国三卷高考试题中导数问题的研究XXX摘要：导数知识是高中数学新教材新增内容之一，导数具有丰富的物理背景和广泛的应用价值，是研究函数问题最重要的工具。在全国三卷高考导数试题中主要包含了函数单调性、极值、零点、不等式等问题，其中在研究函数单调性、极值、零点、不等式等方面的问题中导数具有重要的作用。学生在解答这些相关问题时运用定义法只能讨论简单的函数单调性、极值、零点问题，而运用导数研究能使问题简单化，在使用初等方法证明初等不等式时，会出现很难证明或证明不出来这些情况。那么，引入导数，就会让初等不等式的证明思路变得清晰，证明步骤变得简单.初等不等式证明方法多种多样，导数是其中一个有效且重要的工具。论文具体从用导数求函数的单调性，极值，零点、用导数分析含参数的单调性，极值，零点及知函数的单调性用导数求参数范围和单调性在不等式证明中的应用作了初步探究，叙述了利用导数的定义、函数的单调性等方法来证明初等不等式，指出了上述方法的操作步骤和范围，并总结了证明方法的一般原理。本论文主要通过对全国三卷试题的分析，抛砖引玉得出相应的解题思路帮助学生更容易的掌提导数在高考试题中的应用，帮助学生更快、更好地分析导数的相关知识。关键词：高考导数：函数：单调性：不等式：解题策略Abstract:Derivative knowledge is one of the new content of new high school mathematicstextbooks.Derivative has rich physical background and extensive application value,and it is themost important tool to study function problems.In the three volumes of the national collegeentrance examination,the function monotonicity,extreme value,zero point,inequality and otherproblems,which plays an important role in studying the problems of function monotonicity,extreme value,zero point,inequality and so on.When students answer these related questions,theuse of definition method can only discuss simple function monotonicity,extreme value,zero pointproblems,and the use of derivative research can simplify the problem,in the use of the primarymethod to prove the primary inequality,it will be difficult to prove or not to prove thesesituations.Then,introducing derivatives makes the proof idea of the elementary inequality clearand the proof step simple.There are various methods of elementary inequality proof,andderivatives are an effective and important tool.From the application of derivative monotonicity,extreme value,zero,derivative analysis including parameter monotony,extreme value,zero andknown function,describes the definition of the derivative,function to prove the elementaryinequality,points out the operation steps and range,and summarizes the general principle of proofmethod.This paper mainly through the analysis of the national three volumes of questions,thecorresponding ideas to help students more easily master the application of derivative in the exam,help students to analyze the derivative knowledge faster and better.Key words:college entrance examination derivative;function;monotonicity;inequality;problem solving strategy目录1绪论1.】研究背景…1.1.1导数在高中数学中的现状1.1.2全国三卷高考试题中导数的地位21.1.3导数解题策略在试题中的作用.21.2研究意义和应用价值.…21.2.1研究意义..21.2.2应用价值….31.3国内外研究现状.41.4高中导数的考试大纲.2高考全国三卷导数试题解题研究521导数几何意义试题解题研究.52.1.1在某点处的切线….62.1.2过某点处的切线.72.2导数性态问题解题研究.82.3导数研究函数极值问题112.4导数研究函数零，点问题122.5导数研究不等式问题143结论.163.1主要发现…163.2启示….163.3局限性173.4努力方向17致谢语..18参考文献..19