6 Questions in Survey of Calculus II - Quiz 3 | MTH 126, Quizzes of Calculus

Download 6 Questions in Survey of Calculus II - Quiz 3 | MTH 126 and more Quizzes Calculus in PDF only on Docsity! MTH 126 Name: SS 2007 PID: Quiz 3 Section: Date: Mon., Feb. 26, 2007 (1) (1 Point) The graph of the function z = f(x, y) is given by the following surface: -1 -0.5 0 0.5 1 x -1 -0.5 0 0.5 1 y 0 0.2 0.4 0.6 0.8 1 z (a) Is fx(0.5, 0.5) positive or negative? (b) Is fy(0.5, 0.5) positive or negative? (2) (2 Points) The following table gives values of a positive function f(x, y), with which answer the questions. Show your work! x=0 x = 10 x = 20 x = 30 y=0 89 80 74 71 y=2 93 85 80 76 y=4 98 91 85 81 y=6 104 98 92 88 y=8 112 105 99 94 (a) Estimate fx(20, 4). (b) Estimate fy(20, 4). 1 (3) (3 Points) The retail price z = P (x, y) (in $) of a Ford Taurus is a function of the two variables: x = year of production, y = mileage (in thousand miles). Suppose you know that: P (1997, 70) = 8375, Px(1997, 70) = 1275, Py(1997, 70) = −37.50. (a) What are the units of Px and Py? (b) Interpret Px(1997, 70) = 1275 in practical terms. (c) Estimate the retail price of a 1999 Ford Taurus with 50,000 miles. Show your work! (4) (1 Point) The contour diagram of the function z = f(x, y) is given below. 0 6 12 18 24 x0 25 50 75 100 125 y z = 120 z = 90 z = 60 Estimate the value of fx(12, 75). Show your work! 2