托馬斯微積分課件31 Extreme Values of Functions

Chapter3ApplicationsofDerivatives3.3TheShapeofaGraph3.1ExtremeValuesofFunctions3.2TheMeanValueTheoremandDifferentialEquations3.4GraphicalSolutionsofAutonomousDifferentialEquations3.5ModelingandOptimization3.6LinearizationandDifferentials3.7Newton’sMethod3.1ExtremeValuesofFunctions3.1.1TheDrilling-DigProblem3.1.2Absolute(Global)ExtremeValues3.1.3Local(Relative)ExtremeValues3.1.4FindingExtremeValues3.1.1TheDrilling-DigProblem油井問題Example1.用輸油管把離岸12英里的一座油井和沿岸往下20英里處的煉油廠連接起來(參見附圖)。如果水下輸油管的鋪設(shè)成本為每英里50000美元，而陸地輸油管的鋪設(shè)成本為每英里30000美元。水下和陸地輸油管怎么樣組合才能使連接費用最少？50000美元30000美元1.SmallestamountofunderwaterpipeDollarcost2.AllpipeunderwaterDollarcost3.SomethinginbetweenDollarcost3.1.2Absolute(Global)ExtremeValues絕對極值（最值）Example2.Example3.定理1.閉區(qū)間上連續(xù)的函數(shù)必定取到最大值與最小值。Example4.ExtremeDependingonContinuityonClosedInterval3.1.3Local(Relative)ExtremeValues相對極值（極值）LocalMaximumValuePointLocalMinimumValuePointisnotaextremevaluepointHowtofindextremevalue?Allkindsofthepointswherethefunctionachievesextremevalues.1.Criticalpoint2.EndpointofthedomainoffExample5.FindtheabsolutemaximumandminimumvaluesofontheintervalSolution.1.Criticalpoint2.EndpointExample5.FindtheabsolutemaximumandminimumvaluesofontheintervalExample6.Findtheabsolutemaximumandminimumvaluesof.Solution.1.Criticalpoint2.Endpointmaxormin?Example7.FindtheabsolutemaximumandminimumvaluesofontheintervalSolution.1.Criticalpoint2.EndpointExample7.FindtheabsolutemaximumandminimumvaluesofontheintervalTherelationbetweencriticalpointandextremevaluepointSupposedalocalmaximumvalueACriticalPointACriticalPointSo,criticalpointsneednotgiveextremevalues.Example1.用輸油管把離岸12英里的一座油井和沿岸往下20英里處的煉油廠連接起來(參見附圖)。如果水下輸油管的鋪設(shè)成本為每英里50000美元，而陸地輸油管的鋪設(shè)成本為每英里30000美元。水下和陸地輸油管怎么樣組合才能使連接費用最少？1,200,000dollars1,166,190dollars1,081,025dollarsOurgoalnowistofindtheminimumvalueofc(y).orCriticalpointEndpointTheleastexpensiveconnectioncosts1,080,000dollars,andweachieveitbyrunningthelineunderwatertothepo