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APPLICATIONOFDERIVATIVES

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

1.DERIVATIVEASARATEMEASURE

1.Introduction:averagerateandinstantaneousrate

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

1.DERIVATIVEASARATEMEASURE

2.Rateofchangeingeometry

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

1.DERIVATIVEASARATEMEASURE

3.Rateofchangeinmotion

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

1.DERIVATIVEASARATEMEASURE

44.Rateofchangeincostandrevenue

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

2.INTERPRETATIONOFDY/DXASARATEMEASURE

1.Ratewhendimensionsareincreasingordecreasing

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

2.INTERPRETATIONOFDY/DXASARATEMEASURE

2.Sunlightpoleheightproblem

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

2.INTERPRETATIONOFDY/DXASARATEMEASURE

3.kiteproblemstickonwallinsleeping

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

2.INTERPRETATIONOFDY/DXASARATEMEASURE

4.ProblemofWaterflow

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

93.APPROXIMATIONS

1.Differentialsdefinitions(intermsofsmallchange)andexamples

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

3.APPROXIMATIONS

2. Absolute error; relative error and percentage error and Geometric meaning ofdifferentialsandalgorithm

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

3.APPROXIMATIONS

3.Timeperiodofpendulumproblem

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

3.APPROXIMATIONS

4.Calculationofapproximatevalue

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

3.APPROXIMATIONS

5.Calculationofsquarerootandcuberoot

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

3.APPROXIMATIONS

6.Findtheleastvalueofkforwhichthefunctionx2 + kx + 1isanincreasingfunctionintheinterval1 < x < 2

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

4.MEANVALUETHEOREMS

1.Rolletheorem:statementordefinition

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

4.MEANVALUETHEOREMS

2.Geometricmeaningofrollestheoremanditsuse

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

4.MEANVALUETHEOREMS

3.Applicabilityofrollestheorem

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

4.MEANVALUETHEOREMS

4.VerifyRollTheorem

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

4.MEANVALUETHEOREMS

5.DeterminesolutionofequationusingRolleTheorem

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

4.MEANVALUETHEOREMS

6.LMVT:Statement;proofandGeometricalinterpretation

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

4.MEANVALUETHEOREMS

7.VerificationofLMVT

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

4.MEANVALUETHEOREMS

8.ProveinequalitiesusingLMVT

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

234.MEANVALUETHEOREMS

9.Cauchysmeanvaluetheorem

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

5.EQUATIONOFTANGENTSANDNORMALS

1.Slopeoftangentandnormal

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

5.EQUATIONOFTANGENTSANDNORMALS

2.Equationofnormalandtangents

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

5.EQUATIONOFTANGENTSANDNORMALS

3.Findingtheequationsoftangentandnormaltoacurveatapoint

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

5.EQUATIONOFTANGENTSANDNORMALS

4.Lengthoftangent;normal;subtangentandsubnormal

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

5.EQUATIONOFTANGENTSANDNORMALS

5.Findingtheequationsoftangentandnormalparallelorperpendiculartoagivenline

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

5.EQUATIONOFTANGENTSANDNORMALS

6.Findingtheequationofthecurve

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

6.ANGLEBETWEENTHECURVES

1.Anglebetweentwocurves:howitisequaltoanglebetweentangents

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

6.ANGLEBETWEENTHECURVES

2.Showthatthecurvesx = y2andxy = kcutatrightangles;if8k2 = 1

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

7.MISCELLANEOUSAPPLICATION

1. Find the possible values of p such that the equation px2 = lnx has exactly onesolution.

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

8.MONOTONOCITY

1.Whatisincreasingordecreasingfunction

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

8.MONOTONOCITY

2. Find the locus of point on the curve y2 = 4a x + asinxa

where tangents are

paralleltotheaxisofx

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

8.MONOTONOCITY

3.Solve:4x3 - 24x2 + 44x - 24 > 0

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( ( ))

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

8.MONOTONOCITY

4.Strictlyincreasingfunctionsandstrictlydecreasingfunctions

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

8.MONOTONOCITY

5.Showthatthefunctionf(x) = x2 isneitherstrictly increasingnorstrictlydecreasingonR.

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

8.MONOTONOCITY

6.Letfbecontinuouson[a; b]anddifferentiableon(a; b)Iff(x)isstrictlyincreasingon(a; b) then f′ (x) > 0 for all x ∈ (a; b) and if f(x) is strictly decreasing on (a; b) thenf′ (x) < 0forallx ∈ (a; b)

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

8.MONOTONOCITY

7.Letfbeadifferentiablerealfunctiondefinedon(a; b)andiff′ (x) > 0forallx ∈ (a; b)thenfisincreasingon(a; b)andiff′ (x) < 0forallx ∈ (a; b)thenf(x)isdecreasingon(a; b)

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

8.MONOTONOCITY

8.Findtheintervalsinwhichf(x) =xlogx

isincreasingordecreasing

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

9.MAXIMAANDMINIMA

1.Maximumandminimumvalueoffunctioninitsdomain

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

9.MAXIMAANDMINIMA

2.Findmaximumandminimumvalue;ifany;forf(x)=-|x-1|+5forallxinR

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

10.TESTSFORLOCALMAXIMUM/MINIMUM

1.Localmaximumandlocalminimumandconditionforit

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

10.TESTSFORLOCALMAXIMUM/MINIMUM

2.Conditionofextremum

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

10.TESTSFORLOCALMAXIMUM/MINIMUM

3.Firstderivativetestforlocalmaximaandminima(methodandhowitcomes)

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

10.TESTSFORLOCALMAXIMUM/MINIMUM

4.Higherorderderivativetest

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

10.TESTSFORLOCALMAXIMUM/MINIMUM

5.Findallthepointsoflocalmaximaandminimaofthef(x)=x^3-6x^2+9x-8

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

11.TESTSFORGLOBALMAXIMUM/MINIMUM

1.GlobalMaximumandMinimumandtherequiredcondition

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

12.POINTOFINFLECTION

1.Pointofinflectionandpointofinflexion

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

13.PROPERTIESOFMAXIMAANDMINIMA

1.Propertiesofmaximaandminima

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

14.APPLICATIONOFEXTREMUM

1.Maximaandminimaincloseinterval

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

14.APPLICATIONOFEXTREMUM

2.ApplicationsofMaximaandminimainGeometry

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

14.APPLICATIONOFEXTREMUM

3.ApplicationsofMaximaandminimainalgebra

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

14.APPLICATIONOFEXTREMUM

4.ApplicationsofMaximaandminimaintrigonometry

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

14.APPLICATIONOFEXTREMUM

5. Find two positive numbers whose sum is 14 and the sum of whose squares isminimum

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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES

14.APPLICATIONOFEXTREMUM

6.Findthepointonthecurvey^2=4xwhichisnearesttothepoint(2;-8)

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