31. Rolle's Theorem can be applied to f(x) = /x - 3) on the interval [-2, 8]. A. True B. False 32. Find two positive numbers such that the sum of the first and twice the second is 56 and whose product is a maximum. A. 28 and 28 B. 28 and 14 C. 22 and 17 D. 34 and 11 33. Find the linear approximation of /(x) = 3x2 - 2x at x = 1. A. L(x) = 4x B. L(x) = 4x - 3 C. L(x) = 1 + 4x D. L(x) = 4x + 4 34. Use Newton's Method to approximate the zero for the function ((x) = x -2vx +2 using the initial guess 5. Round your answer to three decimal places. A. 5.464 B. 5.496 C. 5.401 D. 5.515 35. Determine whether the Mean Value Theorem can be applied to the function / (x) = 3x2+ 2x + 5 on the interval [-1, 1]. If the Mean Value Theorem can be applied, find all numbers c in the interval (-1, 1) such that ?'(c) - "(!) - (1) A. The Mean Value Theorem applies; c = 0 B. The Mean Value Theorem applies; - 2 C. The Mean Value Theorem applies; - - 7 6 - 7 D. The Mean Value Theorem does not apply 36. Determine the open intervals on which the graph of f (x) = 3x2 + 7x - 3 is concave upward. A. (-10,0) B. (-60, 1) C. (-BC, 10 ) D. (0,20) 37. Which of the following statements is true about the graph of the function ((x) - - 4 A. The x-intercepts are 2 and -2. B. There are vertical asymptotes at x = 2 and x = -2. C. There are no horizontal asymptotes. D. The domain is all real numbers.commar 38. Complete two iterations of Newton's Method for the function f (x) = x2 - 7 using the initial guess 2.6. Round your answers to four decimal places. A. 2.6463, 2.6460 B. 2.6463, 2.6456 C. 2.6462, 2.6459 D. 2.6462, 2.6458 39. Find the point on the graph of y = 4x + 7 that is closest to the origin. A. (-7.0 B. (-17' 17) C. (-1, 3) D. (-3.1 ) 40. If c is a critical number of the function f, and if f '(x) changes from positive to negative at c, then fhas a relative minimum at c. A. True B. False 41. Locate the absolute extrema of the function g(x) = cos(ir x) on the closed interval (". 2] A. Absolute max (0, 1); Absolute min (2:0) B. Absolute max (2.0) : Absolute min (0. 1) C. Absolute max (2.0) ; No Absolute min D. No Absolute max ; Absolute min (0. 1) 42. Find all points of inflection on the graph of the function f (x) = 4x3 - 5x2+ 5x - 7. A. inflection point at * - -15 B. inflection point at * - 12 C. inflection point at * = -24 D. inflection point at * - 24 43. Rolle's Theorem can be applied to f (x) = x2 on the interval [-3, 3]. A. True B. False 44. Find the open intervals where the function / (x) = x4 - 2x2+ 3 is increasing or decreasing. A. Increasing on (-1, 0) and (1.90) , Decreasing on (-oo, -1) and (0, 1) B. Increasing on (-1,90) , Decreasing on (-90, -1) C. Increasing on (0, 1) and (-, -1), Decreasing on (1,) and (-1, 0) D. Increasing on (1,90) , Decreasing on (-20, 1)5. The measurement of the base and altitude of a triangle are found to be 54 and 33 centimeters. The possible error in each measurement is 0.25 centimeter. Use differentials to estimate the propagated error in computing the area of the triangle. Round your answer to four decimal places. A. +11.9625 square centimeters B. 19.7875 square centimeters C. #10.8750 square centimeters D. +12.5063 square centimeters 46. The edge of a cube is 18 inches with a possible measurement error of 0.1 inch. Find the maximum possible error in calculating the surface area of the cube. A. 5.3 square inches B. 34.7 square inches C. 18.1 square inches D. 21.6 square inches 47. Find the point on the graph of f (x) = 25 - x2 that is closest to the point (1, 0). Round to three decimal places. A. (3.613, 11.946) B. (4.960, 0.398) C. (2.744, 17.470) D. (2.744 0.479) 48. Analyze and sketch a graph of the function y = x3 - 3x2 + 3 A. B. C. D.49. A company introduces a new product for which the number of units sold S is s(1) = 300 8 - 10 6 + t) where t is the time in months since the product was introduced. During what month does S'(t) equal the average rate of change of S(t) during the first year? A. November B. March C. May D. June 50. Find the differential dy of the function y = 2x 3/7 A. dy = =x-4/ dx 3 -4/7 dx B. dy = -=x " C. dy = =x4 D. dy = -: _2x-4/7 dx