1. Homework Homework Assignment #11 Read Section 3.3 Page 139, Exercises: 1 – 73 (EOO), 71 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

2. Homework, Page 139 Compute f ′ (x) using the limit definition. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

3. Homework, Page 139 Compute f ′ (x) using the limit definition. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

4. Homework, Page 139 Use the Power Rule to compute the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

5. Homework, Page 139 Use the Power Rule to compute the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

6. Homework, Page 139 Compute f ′ (a) and find an equation of the tangent line to the graph at x = a. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

7. Homework, Page 139 21. Calculate: Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

8. Homework, Page 139 Calculate the derivative of the function. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

9. Homework, Page 139 Calculate the derivative of the function. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

10. Homework, Page 139 Calculate the derivative of the function. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

11. Homework, Page 139 Calculate the derivative of the function. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

12. Homework, Page 139 Calculate the derivative indicated. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

13. Homework, Page 139 Calculate the derivative indicated. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

14. Homework, Page 139 49. Sketch the graph of f ′(x) for f (x) omitting points where f (x) is not differentiable. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

15. Homework, Page 139 53. Find the points on the curve y = x 2 + 3x – 7 at which the slope of the tangent line is equal to 4.. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

16. Homework, Page 139 57. Determine the coefficients a and b such that p(x) = x 2 + ax + b satisfies p(1) = 0 and p′(1) =4. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

17. Homework, Page 139 61. Compute the derivative of f (x) = x –2 using the limit definition. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

18. Homework, Page 139 65. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

19. Homework, Page 139 69. Let L be a tangent line to the hyperbola xy = 1 at x = a, where a > 0. Show that the area of the triangle bounded by L and the coordinate axes does not depend upon a. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

20. Homework, Page 139 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company 71. Match the functions (A – C) with their derivatives (I – III) in Figure 18. A – III B – I C – II

21. Homework, Page 139 73. Make a rough sketch of the graph of the derivative of the function shown in Figure 19(A). Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

22. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company Chapter 3: Differentiation Section 3.3: Product and Quotient Rules Jon Rogawski Calculus, ET First Edition

23. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company As noted above, the derivative of a product is NOT the product of the derivatives.

24. Example, Page 148 Use the Product Rule to find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

25. Example, Page 148 Use the Product Rule to find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

26. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company As noted above, the derivative of a quotient is NOT the quotient of the derivatives.

27. Example, Page 148 Use the Quotient Rule to find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

28. Example, Page 148 Use the Quotient Rule to find the derivative, then evaluate. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

29. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company The power P delivered to load R by the battery (V and r are constants) is: (a) Calculate dP/dR; (b) Find the value of R where the tangent to the graph of P is horizontal.

30. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

31. Homework Homework Assignment #12 Read Section 3.4 Page 148, Exercises: 1 – 45 (EOO Rogawski Calculus Copyright © 2008 W. H. Freeman and Company