 # Homework Homework Assignment #21 Review Sections 3.1 – 3.11 Page 207, Exercises: 1 – 121 (EOO), skip 73, 77 Chapter 3 Test next time Rogawski Calculus.

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Homework Homework Assignment #21 Review Sections 3.1 – 3.11 Page 207, Exercises: 1 – 121 (EOO), skip 73, 77 Chapter 3 Test next time Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 1.Compute the average ROC of f (x) over [0, 2]. What is the graphical interpretation of this average ROC? Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Compute f ′ (a) using the limit definition and find an equation of the tangent line to the graph of f (x) at x = a. 5. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Compute dy/dx using the limit definition. 9. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Express the limit as a derivative. 13. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 17. Find f (4) and f ′(4) if the tangent line to the graph of f (x) at x = 4 has an equation y = 3x – 14. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 21. A girl’s height h(t) (in cm) is measured at time t (years) for 0 ≤ t ≤ 14: 52, 75.1, 87.5, 96.7, 104.5, 111.8, 118.7, 125.2, 131.5, 137.5, 143.3, 149.2, 155.3, 160.8, 164.7 (a) What is the girl’s average rate of growth over the 14-yr period? (b) Is the average growth rate larger over the first half or second half of this period?

Homework, Page 207 21. Estimate h′(t) (in cm/yr ) for t = 3, 8. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 25. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Compute the derivative. 29. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Compute the derivative. 33. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Compute the derivative. 33. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Compute the derivative. 37. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Compute the derivative. 41. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Compute the derivative. 45. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Compute the derivative. 49. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Compute the derivative. 53. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Find the derivative. 57. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Find the derivative. 61. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Find the derivative. 65. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Find the derivative. 69. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Use the table of values to calculate the derivative of the given function at x = 2. 81. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company xf (x)g (x)f ′ (x)g ′ (x) 254–39 432–23

Homework, Page 207 Let f (x) = x 3 – 2x 2 + x + 1. 85. Find the points on the graph where the tangent line has a slope of 10 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Let f (x) = x 3 – 2x 2 + x + 1. 89. (a) Show that there is a unique value of a such that f (x) has the same slope at both a and a + 1. (b) Plot f (x) together with the tangent lines at x = a and x = a + 1 and confirm the answer in part (a). Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Calculate y″. 93. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 97.In Figure 5, label f, f ′, and f ″. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Compute dy/dx. 101. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 Compute dy/dx. 105. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 109. Find the points on the graph of x 3 – y 3 = 3xy – 3 where the tangent line is horizontal. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 113. Water pours into the tank in Figure 7 at a rate of 20 m 3 /min. How fast is the water level rising when the eater level is h = 4m? Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 117. (a) Side x of the triangle in Figure 9 is increasing at 2 cm/s and side y is increasing at 3 cm/s. Assume that θ decreases in such a way that the area of the triangle has a constant value of 4 cm 2. How fast is θ decreasing when x = 4, y = 4? Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 117. (a) Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 207 117. (b) How fast is the distance between P and Q changing when x = 2, y = 3? Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 197 Use logarithmic differentiation to find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

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