Active Calculus - Gvsu - Grand Valley State University

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88 3.5. RELATED RATES
Chapter 4The Definite Integral4.1 Determining distance traveled from velocityPreview Activity 4.1. Suppose that a person is taking a walk along a long straight path and walksat a constant rate of 3 miles per hour.(a) On the left-hand axes provided in Figure 4.1, sketch a labeled graph of the velocity functionv(t) = 3. Note that while the scale on the two sets of axes is the same, the units on the right-8mph8miles44hrshrs1 21 2Figure 4.1: At left, axes for plotting y = v(t); at right, for plotting y = s(t).hand axes differ from those on the left. The right-hand axes will be used in question (d).(b) How far did the person travel during the two hours? How is this distance related to thearea of a certain region under the graph of y = v(t)?(c) Find an algebraic formula, s(t), for the position of the person at time t, assuming thats(0) = 0. Explain your thinking.89
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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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1.6. THE SECOND DERIVATIVE 23• on
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1.6. THE SECOND DERIVATIVE 25ffxxf
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1.7. LIMITS, CONTINUITY, AND DIFFER
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1.7. LIMITS, CONTINUITY, AND DIFFER
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1.8. THE TANGENT LINE APPROXIMATION
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Chapter 2Computing Derivatives2.1 E
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2.1. ELEMENTARY DERIVATIVE RULES 35
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Active Calculus - Gvsu - Grand Valley State University

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