Active Calculus - Gvsu - Grand Valley State University

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66 3.1. USING DERIVATIVES TO IDENTIFY EXTREME VALUES OF A FUNCTION(f) Identify all values of c for which h ′ (c) does not exist.(g) True or false: every relative maximum and minimum of h occurs at a point where h ′ (c) iseither zero or does not exist.(h) True or false: at every point where h ′ (c) is zero or does not exist, h has a relative maximumor minimum.⊲⊳
3.1. USING DERIVATIVES TO IDENTIFY EXTREME VALUES OF A FUNCTION 67Activity 3.1.Suppose that g(x) is a function continuous for every value of x ≠ 2 whose first derivative isg ′ (x + 4)(x − 1)2(x) = . Further, assume that it is known that g has a vertical asymptote atx − 2x = 2.(a) Determine all critical values of g.(b) By developing a carefully labeled first derivative sign chart, decide whether g has as alocal maximum, local minimum, or neither at each critical value.(c) Does g have a global maximum? global minimum? Justify your claims.(d) What is the value of limx→∞ g′ (x)? What does the value of this limit tell you about thelong-term behavior of g?(e) Sketch a possible graph of y = g(x).⊳
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Active CalculusMatt Boelkins, Lead
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Chapter 1Understanding the Derivati
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1.1. HOW DO WE MEASURE VELOCITY? 3A
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1.2. THE NOTION OF LIMIT 51.2 The n
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1.2. THE NOTION OF LIMIT 7Activity
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1.3. THE DERIVATIVE OF A FUNCTION A
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1.3. THE DERIVATIVE OF A FUNCTION A
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1.4. THE DERIVATIVE FUNCTION 131.4
Page 19 and 20: 1.4. THE DERIVATIVE FUNCTION 15rsxx
Page 21 and 22: 1.5. INTERPRETING THE DERIVATIVE AN
Page 23 and 24: 1.5. INTERPRETING THE DERIVATIVE AN
Page 25 and 26: 1.6. THE SECOND DERIVATIVE 21(a) In
Page 27 and 28: 1.6. THE SECOND DERIVATIVE 23• on
Page 29 and 30: 1.6. THE SECOND DERIVATIVE 25ffxxf
Page 31 and 32: 1.7. LIMITS, CONTINUITY, AND DIFFER
Page 33 and 34: 1.7. LIMITS, CONTINUITY, AND DIFFER
Page 35 and 36: 1.8. THE TANGENT LINE APPROXIMATION
Page 37 and 38: Chapter 2Computing Derivatives2.1 E
Page 39 and 40: 2.1. ELEMENTARY DERIVATIVE RULES 35
Page 41 and 42: 2.2. THE SINE AND COSINE FUNCTIONS
Page 43 and 44: 2.2. THE SINE AND COSINE FUNCTIONS
Page 45 and 46: 2.3. THE PRODUCT AND QUOTIENT RULES
Page 47 and 48: 2.3. THE PRODUCT AND QUOTIENT RULES
Page 49 and 50: 2.4. DERIVATIVES OF OTHER TRIGONOME
Page 51 and 52: 2.4. DERIVATIVES OF OTHER TRIGONOME
Page 53 and 54: 2.5. THE CHAIN RULE 492.5 The chain
Page 55 and 56: 2.5. THE CHAIN RULE 51Activity 2.14
Page 57 and 58: 2.6. DERIVATIVES OF INVERSE FUNCTIO
Page 59 and 60: 2.6. DERIVATIVES OF INVERSE FUNCTIO
Page 61 and 62: 2.7. DERIVATIVES OF FUNCTIONS GIVEN
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Page 65 and 66: 2.8. USING DERIVATIVES TO EVALUATE
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Page 69: Chapter 3Using Derivatives3.1 Using
Page 73 and 74: 3.1. USING DERIVATIVES TO IDENTIFY
Page 75 and 76: 3.2. USING DERIVATIVES TO DESCRIBE
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Page 79 and 80: 3.3. GLOBAL OPTIMIZATION 75Activity
Page 81 and 82: 3.3. GLOBAL OPTIMIZATION 77Activity
Page 83 and 84: 3.4. APPLIED OPTIMIZATION 79Activit
Page 85 and 86: 3.4. APPLIED OPTIMIZATION 81Activit
Page 87 and 88: 3.5. RELATED RATES 833.5 Related Ra
Page 89 and 90: 3.5. RELATED RATES 85Activity 3.15.
Page 91 and 92: 3.5. RELATED RATES 87Activity 3.17.
Page 93 and 94: Chapter 4The Definite Integral4.1 D
Page 95 and 96: 4.1. DETERMINING DISTANCE TRAVELED
Page 97 and 98: 4.1. DETERMINING DISTANCE TRAVELED
Page 99 and 100: 4.2. RIEMANN SUMS 95⊲⊳
Page 101 and 102: 4.2. RIEMANN SUMS 97Activity 4.5.Su
Page 103 and 104: 4.3. THE DEFINITE INTEGRAL 994.3 Th
Page 105 and 106: 4.3. THE DEFINITE INTEGRAL 101Activ
Page 107 and 108: 4.3. THE DEFINITE INTEGRAL 103Activ
Page 109 and 110: 4.4. THE FUNDAMENTAL THEOREM OF CAL
Page 111: 4.4. THE FUNDAMENTAL THEOREM OF CAL
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Active Calculus - Gvsu - Grand Valley State University

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