Student Solutions Manual
to accompany
Calculus for Business,
Economics, and the
Social and Life Sciences
Tenth Edition, Brief
Laurence D. Hoffman
Smith Barney
Gerald L. Bradley
Claremon McKenna College
Prepared by
Devilyna Nichols
Purdue University
,[to rwbe rwsupplied rwby rwpublisher]
,CONTENTS
Chapter Functions, rwGraphs, rwand 1
rw1 rwLimits
1.1 Functions 1
1.2 The rwGraph rwof rwa rwFunction6
1.3 Linear rwFunctions 14
1.4 Functional rwModels 19
1.5 Limits 26
1.6 One-Sided rwLimits rwand 30
rwContinuity
Checkup rwfor rwChapter rw1 33
Review rwProblems 36
Chapter rw2 rw rw r w Differentiation: rwBasic rwConcepts 43
2.1 The rwDerivative 43
2.2 Techniques rwof r w Differentiation 52
2.3 Product rwand rwQuotient rwRules; rwHigher-Order rwDerivatives57
2.4 The rwChain rwRule 64
2.5 Marginal rwAnalysis; rwApproximations rwUsing rwIncrements72
2.6 Implicit rwDifferentiation rwand rwRelated rwRates75
Checkup rwfor rwChapter rw2 82
Review rwProblems 84
Chapter rw3 rw rw r w Additional rwApplications rwof rwthe rwDerivative 93
3.1 Increasing rwand rwDecreasing rwFunctions; rwRelative rwExtrema93
3.2 Concavity rwand rwPoints rwof rwInflection103
3.3 Curve rwSketching 114
3.4 Optimization 124
3.5 Additional rwApplied rwOptimization 132
Checkup rwfor rwChapter rw3 141
Review rwProblems 148
Chapter rw4 rw rw r w Exponential rwand rwLogarithmic rwFunctions 159
4.1 Exponential rwFunctions 159
4.2 Logarithmic rwFunctions 165
4.3 Differentiation rwof rwLogarithmic rwand rwExponential rwFunctions173
4.4 Additional rwExponential rwModels 182
Checkup rwfor rwChapter rw4 199
Review rwProblems 205
, iii
iv Contents
Chapter rw5 rw rw r w Integration 219
5.1 Antidifferentiation; rwthe rwIndefinite rwIntegral 219
5.2 Integration rwby rwSubstitution 226
5.3 The rwDefinite rwIntegral rwand rwthe rwFundamental rwTheorem rwof rwCalculus 233
5.4 Applying rwDefinite rwIntegration: rwArea rwBetween rwCurves rwand rwAverage rwValue 238
5.5 Additional rwApplications rwto rwBusiness rwand rwEconomics 245
5.6 Additional rwApplications rwto rwthe rwLife rwand rwSocial rwSciences 252
Checkup rwfor rwChapter rw5 259
Review rwProblems 262
Chapter rw6 rw rw r w Additional rwTopics rwin rwIntegration 273
6.1 Integration rwby rwParts; rwIntegral rwTables 273
6.2 Introduction rwto rwDifferential rwEquations 284
6.3 Improper rwIntegrals; rwContinuous rwProbability 292
6.4 Numerical rwIntegration 300
Checkup rwfor rwChapter rw6 307
Review rwProblems 312
Chapter rw7 rw rw r w Calculus rwof rwSeveral rwVariables 325
7.1 Functions rwof rwSeveral rwVariables 325
7.2 Partial rwDerivatives 329
7.3 Optimizing rwFunctions rwof rwTwo rwVariables 336
7.4 The rwMethod rwof rwLeast rwSquares346
7.5 Constrained rwOptimization: rwThe rwMethod rwof rwLagrange rwMultipliers 353
7.6 Double rwIntegrals 362
Checkup rwfor rwChapter rw7 371
Review rwProblems 375
to accompany
Calculus for Business,
Economics, and the
Social and Life Sciences
Tenth Edition, Brief
Laurence D. Hoffman
Smith Barney
Gerald L. Bradley
Claremon McKenna College
Prepared by
Devilyna Nichols
Purdue University
,[to rwbe rwsupplied rwby rwpublisher]
,CONTENTS
Chapter Functions, rwGraphs, rwand 1
rw1 rwLimits
1.1 Functions 1
1.2 The rwGraph rwof rwa rwFunction6
1.3 Linear rwFunctions 14
1.4 Functional rwModels 19
1.5 Limits 26
1.6 One-Sided rwLimits rwand 30
rwContinuity
Checkup rwfor rwChapter rw1 33
Review rwProblems 36
Chapter rw2 rw rw r w Differentiation: rwBasic rwConcepts 43
2.1 The rwDerivative 43
2.2 Techniques rwof r w Differentiation 52
2.3 Product rwand rwQuotient rwRules; rwHigher-Order rwDerivatives57
2.4 The rwChain rwRule 64
2.5 Marginal rwAnalysis; rwApproximations rwUsing rwIncrements72
2.6 Implicit rwDifferentiation rwand rwRelated rwRates75
Checkup rwfor rwChapter rw2 82
Review rwProblems 84
Chapter rw3 rw rw r w Additional rwApplications rwof rwthe rwDerivative 93
3.1 Increasing rwand rwDecreasing rwFunctions; rwRelative rwExtrema93
3.2 Concavity rwand rwPoints rwof rwInflection103
3.3 Curve rwSketching 114
3.4 Optimization 124
3.5 Additional rwApplied rwOptimization 132
Checkup rwfor rwChapter rw3 141
Review rwProblems 148
Chapter rw4 rw rw r w Exponential rwand rwLogarithmic rwFunctions 159
4.1 Exponential rwFunctions 159
4.2 Logarithmic rwFunctions 165
4.3 Differentiation rwof rwLogarithmic rwand rwExponential rwFunctions173
4.4 Additional rwExponential rwModels 182
Checkup rwfor rwChapter rw4 199
Review rwProblems 205
, iii
iv Contents
Chapter rw5 rw rw r w Integration 219
5.1 Antidifferentiation; rwthe rwIndefinite rwIntegral 219
5.2 Integration rwby rwSubstitution 226
5.3 The rwDefinite rwIntegral rwand rwthe rwFundamental rwTheorem rwof rwCalculus 233
5.4 Applying rwDefinite rwIntegration: rwArea rwBetween rwCurves rwand rwAverage rwValue 238
5.5 Additional rwApplications rwto rwBusiness rwand rwEconomics 245
5.6 Additional rwApplications rwto rwthe rwLife rwand rwSocial rwSciences 252
Checkup rwfor rwChapter rw5 259
Review rwProblems 262
Chapter rw6 rw rw r w Additional rwTopics rwin rwIntegration 273
6.1 Integration rwby rwParts; rwIntegral rwTables 273
6.2 Introduction rwto rwDifferential rwEquations 284
6.3 Improper rwIntegrals; rwContinuous rwProbability 292
6.4 Numerical rwIntegration 300
Checkup rwfor rwChapter rw6 307
Review rwProblems 312
Chapter rw7 rw rw r w Calculus rwof rwSeveral rwVariables 325
7.1 Functions rwof rwSeveral rwVariables 325
7.2 Partial rwDerivatives 329
7.3 Optimizing rwFunctions rwof rwTwo rwVariables 336
7.4 The rwMethod rwof rwLeast rwSquares346
7.5 Constrained rwOptimization: rwThe rwMethod rwof rwLagrange rwMultipliers 353
7.6 Double rwIntegrals 362
Checkup rwfor rwChapter rw7 371
Review rwProblems 375
