The marginal cost of a product can be thought of as the

Chapter 3, Problem 89

(choose chapter or problem)

The marginal cost of a product can be thought of as the cost of producing one additional unit of output. For example, if the marginal cost of producing the 50th product is $6.20, it cost $6.20 to increase production from 49 to 50 units of output. Suppose the marginal cost C Applications and Extensions 73. The graph of the function f1x2 = ax2 + bx + c has vertex at (0, 2) and passes through the point (1, 8). Find a, b, and c. 74. The graph of the function f1x2 = ax2 + bx + c has vertex at (1, 4) and passes through the point (-1, -8). Find a, b, and c. In 7580, for the given functions f and g, (a) Graph f and g on the same Cartesian plane. (b) Solve f1x2 = g1x2. (c) Use the result of part (b) to label the points of intersection of the graphs of f and g. (d) Shade the region for which f1x2 7 g1x2, that is, the region below f and above g. 75. f1x2 = 2x - 1; g1x2 = x2 - 4 76. f1x2 = -2x - 1; g1x2 = x2 - 9 77. f1x2 = -x2 + 4; g1x2 = -2x + 1 78. f1x2 = -x2 + 9; g1x2 = 2x + 1 79. f1x2 = -x2 + 5x; g1x2 = x2 + 3x - 4 80. f1x2 = -x2 + 7x - 6; g1x2 = x2 + x - 6 Answer 81 and 82 using the following: A quadratic function of the form f1x2 = ax2 + bx + c with b2 - 4ac 7 0 may also be written in the form f1x2 = a1x - r12 1x - r22, where r1 and r2 are the x-intercepts of the graph of the quadratic function. Mixed Practice In 6172, (a) graph each function, (b) determine the domain and the range of the function, and (c) determine where the function is increasing and where it is decreasing. 61. f1x2 = x2 - 2x - 15 62. g1x2 = x2 - 2x - 8 63. F1x2 = 2x - 5 64. f1x2 = 3 2 x - 2 65. g1x2 = -21x - 322 + 2 66. h1x2 = -31x + 122 + 4 67. f1x2 = 2x2 + x + 1 68. G1x2 = 3x2 + 2x + 5 69. h1x2 = - 2 5 x + 4 70. f1x2 = -3x + 2 71. H1x2 = -4x2 - 4x - 1 72. F1x2 = -4x2 + 20x - 25 158 CHAPTER 3 Linear and Quadratic Functions (in dollars) to produce x thousand mp3 players is given by the function C(x) = x2 - 140x + 7400 (a) How many players should be produced to minimize the marginal cost? (b) What is the minimum marginal cost?