函数最值问题的求解方法和应用初稿

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1、摘要函数最值问题是重要的分析问题之一。它不仅在教学中解决一些数学问题，而且常运用于解决实际问题.本文探讨了求函数的最值的几种解法，着重介绍了初等数学中的求函数方程的基本解法：判别式法、配方法、均值不等式法、换元法、向量法、单调性法、数形结合法、待定系数法和高等数学中函数方程的解法：导数法、函数的有界性法,同时介绍了求解函数最值时应注意的一些问题，在实际问题的应用过程中不断地熟练掌握这些解法,进一步阐述函数最值问题研究的重要性。关键词：函数最值，初等数学,高等数学，导数ABSTRACTThefunctionofextremumisoneoftheimportantproble

2、msofanalysis.Itnotonlyintheteachingsolvingmathematicalproblems,andoftenusedinsolvingpracticalproblems.Thispaperdiscussesthesolutionofthefunctionofextremum,introducesthebasicmethodtosolvethefunctionequationinElementaryMathematics:Discrimi-nantanalysismethod,completingsquare,themeanvalueineq

3、ualitymethod,methodofsubstitution,vectormethod,themonotonyoffunctionmethod,combiningnumberswithshapesmethod,methodofundeterminedcoefficients,andsolutionofequationsinHigherMathematics:derivativemethod,functionboundednessmethod.Atthesametime,thesolutionofthevaluefunctionandsomeproblemsshould

4、bepaidattentionto,Inordertomakefulluseofthesesolutions,furtherillustratestheimportanceofthevalueofafunction.Keywords:mostvalueoffunction;elementarymathematics;advancedmathematics;derivative目录1引言······································································2求函数最值的几种解法···············

5、·································2.1判别式法·····························································2.2配方法·······························································2.3均值不等式法························································2.4换元法·················································

6、··············2.5向量法································································2.6单调性法·····························································2.7导数法·······························································2.8函数的有界性法······················································2.9数形

7、结合法···························································3求解函数最值时应注意的一些问题··································3.1注意定义域···························································3.2注意值域·····························································3.3注意参变数的约束条件