Active Calculus - Gvsu - Grand Valley State University

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14 1.4. THE DERIVATIVE FUNCTIONActivity 1.10.For each given graph of y = f(x), sketch an approximate graph of its derivative function,y = f ′ (x), on the axes immediately below. The scale of the grid for the graph of f is 1 × 1;assume the horizontal scale of the grid for the graph of f ′ is identical to that for f. If necessary,adjust and label the vertical scale on the axes for the graph of f ′ .fgxxf ′g ′xxpqxxp ′q ′xx
1.4. THE DERIVATIVE FUNCTION 15rsxxr ′s ′xxwzxxw ′z ′xxWrite several sentences that describe your overall process for sketching the graph of the derivativefunction, given the graph the original function. What are the values of the derivative functionthat you tend to identify first? What do you do thereafter? How do key traits of the graphof the derivative function exemplify properties of the graph of the original function?⊳
Page 1: Active CalculusMatt Boelkins, Lead
Page 5 and 6: Chapter 1Understanding the Derivati
Page 7 and 8: 1.1. HOW DO WE MEASURE VELOCITY? 3A
Page 9 and 10: 1.2. THE NOTION OF LIMIT 51.2 The n
Page 11 and 12: 1.2. THE NOTION OF LIMIT 7Activity
Page 13 and 14: 1.3. THE DERIVATIVE OF A FUNCTION A
Page 15 and 16: 1.3. THE DERIVATIVE OF A FUNCTION A
Page 17: 1.4. THE DERIVATIVE FUNCTION 131.4
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
Page 63 and 64: 2.7. DERIVATIVES OF FUNCTIONS GIVEN
Page 65 and 66: 2.8. USING DERIVATIVES TO EVALUATE
Page 67 and 68: 2.8. USING DERIVATIVES TO EVALUATE
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Chapter 3Using Derivatives3.1 Using
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3.1. USING DERIVATIVES TO IDENTIFY
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3.1. USING DERIVATIVES TO IDENTIFY
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3.2. USING DERIVATIVES TO DESCRIBE
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3.2. USING DERIVATIVES TO DESCRIBE
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3.3. GLOBAL OPTIMIZATION 75Activity
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3.3. GLOBAL OPTIMIZATION 77Activity
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3.4. APPLIED OPTIMIZATION 79Activit
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3.4. APPLIED OPTIMIZATION 81Activit
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3.5. RELATED RATES 833.5 Related Ra
Page 89 and 90:
3.5. RELATED RATES 85Activity 3.15.
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3.5. RELATED RATES 87Activity 3.17.
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Chapter 4The Definite Integral4.1 D
Page 95 and 96:
4.1. DETERMINING DISTANCE TRAVELED
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4.1. DETERMINING DISTANCE TRAVELED
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4.2. RIEMANN SUMS 95⊲⊳
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4.2. RIEMANN SUMS 97Activity 4.5.Su
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4.3. THE DEFINITE INTEGRAL 994.3 Th
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4.3. THE DEFINITE INTEGRAL 101Activ
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4.3. THE DEFINITE INTEGRAL 103Activ
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4.4. THE FUNDAMENTAL THEOREM OF CAL
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4.4. THE FUNDAMENTAL THEOREM OF CAL
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Active Calculus - Gvsu - Grand Valley State University

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