Active Calculus - Gvsu - Grand Valley State University

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74 3.3. GLOBAL OPTIMIZATION3.3 Global OptimizationPreview Activity 3.3. Let f(x) = 2 +31 + (x + 1) 2 .(a) Determine all of the critical values of f.(b) Construct a first derivative sign chart for f and thus determine all intervals on which f isincreasing or decreasing.(c) Does f have a global maximum? If so, why, and what is its value and where is the maximumattained? If not, explain why.(d) Determine lim f(x) and lim f(x).x→∞ x→−∞(e) Explain why f(x) > 2 for every value of x.(f) Does f have a global minimum? If so, why, and what is its value and where is the minimumattained? If not, explain why.⊲⊳
3.3. GLOBAL OPTIMIZATION 75Activity 3.7.Let g(x) = 1 3 x3 − 2x + 2.(a) Find all critical values of g that lie in the interval −2 ≤ x ≤ 3.(b) Use a graphing utility to construct the graph of g on the interval −2 ≤ x ≤ 3.(c) From the graph, determine the x-values at which the global minimum and global maximumof g occur on the interval [−2, 3].(d) How do your answers change if we instead consider the interval −2 ≤ x ≤ 2?(e) What if we instead consider the interval −2 ≤ x ≤ 1?⊳
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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
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1.4. THE DERIVATIVE FUNCTION 15rsxx
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1.5. INTERPRETING THE DERIVATIVE AN
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1.5. INTERPRETING THE DERIVATIVE AN
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1.6. THE SECOND DERIVATIVE 21(a) In
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Page 35 and 36: 1.8. THE TANGENT LINE APPROXIMATION
Page 37 and 38: Chapter 2Computing Derivatives2.1 E
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Page 41 and 42: 2.2. THE SINE AND COSINE FUNCTIONS
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Page 45 and 46: 2.3. THE PRODUCT AND QUOTIENT RULES
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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
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Page 69 and 70: Chapter 3Using Derivatives3.1 Using
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Page 95 and 96: 4.1. DETERMINING DISTANCE TRAVELED
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Page 111: 4.4. THE FUNDAMENTAL THEOREM OF CAL
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Active Calculus - Gvsu - Grand Valley State University

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