浅谈导数在高中数学中主要的应用摘要：导数作为研究函数的单调性、变化快慢、最值和极值等问题的最方便的工具，在高中数学中处于一个非常重要的位置。导数的学习为解决高中数学问题提供了新的依据和方法，使学生的数学思维得到发展、解题能力得到提升。导数作为解决高中数学问题的重要工具之一，其相关知识在高考中占有十分重要的地位。同时导数作为微积分的重要内容之一，被认为是现代数学的基本概念，体现了微积分的基本思想，为之后对高等数学的学习奠定了基础。本文将首先阐述高中数学中导数的基本情况，然后通过对高考试题的分析，采取分类讨论的方式，对导数在高中数学中的主要应用进行总结和归纳。包括导数在几何中的应用、导数在函数中的应用、导数在不等式中的应用三个方面，其中较为重要的是导数在几何中的应用和导数在函数中的应用。导数在几何中的应用主要是考查对导数的几何意义的理解和运用；对于导数在不等式中的应用，其实质是导数与函数性质的综合应用。导数能够定量地刻画函数局部变化，是研究函数各种性质的有效工具，本文将从函数的单调性、极值、最值和零点问题四个方面对其进行总结。关键词：导数;高中数学;数学问题AbriefDiscussiononthemainApplicationofDerivativeinSeniorHighSchoolMathematicsAbstract：Asthemostconvenienttooltostudytheproblemsofthemonotonicity,thespeedofchange,themaximumandtheextremevalueoffunction,derivativeisinaveryimportantpositioninseniorhighschoolmathematics.Thelearningofderivativeprovidesanewbasisandapproachforsolvingproblemsinhighschoolmathematics,whichcandevelopthemathematicalthinkingandimprovetheabilityofsolvingproblemsofstudents.Asoneoftheimportanttoolstosolvehighschoolmathematicsproblems,derivativeplaysanveryimportantroleinthecollegeentranceexamination.Atthesametime,asoneoftheimportantcontentsofcalculus,derivativeisconsideredasthebasicconceptofmodernmathematics,whichembodiesthebasicideasofcalculusandlaysthefoundationforthelaterlearningofhighermathematics.Inthispaper,Iwillfirstelaboratethebasicsituationofderivativeinseniorhighschoolmathematics,andthenthroughtheanalysisofcollegeentranceexaminationquestions.Themainapplicationofderivativeinseniorhighschoolmathematicsissummarizedandconcludedbythewayofclassifieddiscussion.Itincludesthreeaspects:theapplicationofderivativeingeometry,theapplicationofderivativeinfunctionandtheapplicationofderivativeininequality,amongwhichtheapplicationofderivativeingeometryandtheapplicationofderivativeinfunctionaremoreimportant.TheapplicationofderivativeingeometryismainlytoexaminetheIunderstandingandapplicationofthegeometricmeaningofderivative.Fortheapplicationofderivativeininequality,itsessenceisthecomprehensiveapplicationofderivativeandfunctionproperties.Derivativeisaneffectivetooltostudythevariouspropertiesoffunction,whichcanquantitativelydescribethelocalchangeoffunction.Inthispaper,Iwillsummarizeitfromthemonotonicity,extremevalue,maximumvalueandzeropointoffunction.Keywords:Derivative;Highschoolmathematics;Mathematicalproblem目录1绪论..............................................................................................................................................11.1选题的背景及意义........................................................................................................11.2国内外研究现状............................................................................................................11.3研究方法......................................................................................................................22高中数学中导数的基本情况.............
