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

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

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

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

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

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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

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

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

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

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

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

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

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

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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

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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

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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

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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

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

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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

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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

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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

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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

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

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

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

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

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

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

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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.

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

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

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