AP Calculus AB review AP微積分復(fù)習(xí)提綱

APCalculusABreviewAP微積分復(fù)習(xí)提綱APCalculusABreviewAP微積分復(fù)習(xí)提綱APCalculusABreviewAP微積分復(fù)習(xí)提綱APCalculusABreviewAP微積分復(fù)習(xí)提綱編制僅供參考審核批準(zhǔn)生效日期地址：電話：傳真:郵編:APCALCULUSABREVIEWChapter2Differentiation DefinitionofTangentLinewithSlopmIffisdefinedonanopenintervalcontainingc,andifthelimit lim exists,thenthelinepassingthrough(c,f(c))withslopemisthetangentlinetothegraphoffatthepoint(c,f(c)).DefinitionoftheDerivativeofaFunctionTheDerivativeoffatxisgivenbyf'providedthelimitexists.Forallxforwhichthislimitexists,f’isafunctionofx.*ThePowerRule*TheProductRule*d*d*TheChainRule?ImplicitDifferentiation(takethederivativeonbothsides;derivativeofyisy*y’)Chapter3ApplicationsofDifferentiation*Extremaandthefirstderivativetest(minimum:?→+,maximum:+→?,+&?arethesignoff’(x))*DefinitionofaCriticalNumberLetfbedefinedatc.Iff’(c)=0ORIFFISNOTDIFFERENTIABLEATC,thencisacriticalnumberoff.*Rolle’sTheoremIffisdifferentiableontheopeninterval(a,b)andf(a)=f(b),thenthereisatleastonenumbercin(a,b)suchthatf’(c)=0.*TheMeanValueTheoremIffiscontinuousontheclosedinterval[a,b]anddifferentiableontheopeninterval(a,b),thenthereexistsanumbercin(a,b)suchthatf’(c)=fb*Increasinganddecreasingintervaloffunctions(takethefirstderivative)*Concavity(ontheintervalwhichf’’>0,concaveup)*SecondDerivativeTestLetfbeafunctionsuchthatf’(c)=0andthesecondderivativeoffexistsonanopenintervalcontainingc.Iff’’(c)>0,thenf(c)isaminimumIff’’(c)<0,thenf(c)isamaximum*PointsofInflection(takesecondderivativeandsetitequalto0,solvetheequationtogetxandplugxvalueinoriginalfunction)*Asymptotes(horizontalandvertical)*LimitsatInfinity*CurveSketching(takefirstandsecondderivative,makesureallthecharacteristicsofafunctionareclear)?OptimizationProblems*Newton’sMethod(usedtoapproximatethezerosofafunction,whichistediousandstupid,DONOTHAVETOKNOWIFUDONOTWANTTOSCORE5)Chapter4&5Integration*Beabletosolveadifferentialequation*BasicIntegrationRules1)u2)sin3)cos4)1*Integralofafunctionistheareaunderthecurve*RiemannSum(divideintervalintoalotofsub-intervals,calculatetheareaforeachsub-intervalandsummationistheintegral).*Definiteintegral*TheFundamentalTheoremofCalculusIfafunctionfiscontinuousontheclosedinterval[a,b]andFisananti-derivativeoffontheinterval[a,b],thenab*DefinitionoftheAverageValueofaFunctiononanIntervalIffisintegrableontheclosedinterval[a,b],thentheaveragevalueoffontheintervalis1b-a*ThesecondfundamentaltheoremofcalculusIffiscontinuousonanopeninternalIcontaininga,then,foreveryxintheinterval,ddx*IntegrationbySubstitution*IntegrationofEvenandOddFunctions1)Iffisanevenfunction,thenab2)Iffisanoddfunction,thenab*TheTrapezoidalRuleLetfbecontinuouson[a,b].ThetrapezoidalRuleforapproximatingabaMoreover,an→∞,theright-handsideapproachesab*Simpson’sRule(niseven)Letfbecontinuouson[a,b].Simpson’sRuleforapproximatingabfaMoreover,asn→∞,theright-handsideapproachesa*Inversefunctions(y=f(x),switchyandx,solveforx)*TheDerivativeofanInverseFunctionLetfbeafunctionthatisdifferentiableonanintervalI.Iffhasaninversefunctiong,thengisdifferentiableatanyxforwhichf’(g(x))≠0.Moreover,g'x=1f'(g(x)*TheDerivativeoftheNaturalExponentialFunctionLetubeadifferentiablefunctionofx.ddxex*IntegrationRulesforExponentialFunctionsLetubeadifferentiablefunctionofx.eu?DerivativesforBasesotherthaneLetabeapositiverealnumber(a≠1)andletubeadifferentiablefunctionofx.1.ddxa?a?lim*Derivativesof