40. Find dy in terms of x and y for the function x + y = 6. dx y a. . X b. 6 dy 2 X N - + y c . a dy y dy 2 12 d. dry dx 2 d'y y e. dx 2 41. The function f(x) = x has two tangents drawn to it at the points on its graph where x = -1 and x = 1. What are the coordinates of the point where the two tangent lines intersect? a. (0, 1) b. (0, 0) C. (0, -1) d. (0, -2) e. none of these 42. The function f(x) = x has two normal lines drawn to it at the points on its graph where x = -1 and x = 1. What are the coordinates of the point where the two normal lines intersect each other? a. (0, 1) b. (0, 0) C. (0, -1) d. (0, -2) e. none of these Unit 2 Evaluation 186 MTHH 07143. A tangent line and a normal line are drawn to the function f(x) = " + 5x + 6 at the x2 - 4 point where x = 3. What is the product of the slopes of the tangent line and the normal line when the function is passing through the point where x = 3 will be? a. -1 b. 0 C. 1 d. 2 e. none of these 44. The equation for the tangent line to a function y = f(x) at (a, f(a)) is a. y = f '( x )y b. y = f '(a) c. y - a = f(x) . (x - a) d. y - fla) = f'(a) . (x - a) JIN 45. Find the equation for the tangent line of f(x) = (x3 + 8 )(2x - 4) at a = 8. a. y - 144 = 28(x - 8) b. y = 28x - 224 c. y - 144 = -16(x - 8) d. y - 144 = 2 (x -8) 46. If f(x) = (3x - 1) "s, then f '(3) = 1 a. True b. False 47. If f(x) = x + x- 2 then f(2) would equal 8. What would the slope of the inverse function to f(x) be when x = 8? a. 8 b. 13 1 d 1 13 e. none of these Unit 2 Evaluation 187 MTHH 07148. Find f '(x) if f(x) = x ( x + 2)?. a. 2x . (x + 2) b. (x + 2)(x + 2x+ 1) c. 4x(x + 2)(x + 1) d. none of these 49. If f(x) is continuous on [a, b], which of the following must be true? 1. f(x) is differentiable on (a, b) Il. f(x) is defined for all x in [a, b] Ill. f(x) has a maximum on (a, b) a. I b. II C. III d. All of these are true. 50. If f(x) is differentiable on (a, b), which of the following must be true? I. f(x) is continuous on (a, b) Il. f(x) is defined for all x in [a, b] Ill. There exists a point c in [a, b] such that f(c) = 0 a. I b. II C. III d. All of these are true. Carefully check your answers on this evaluation and make any corrections you feel are necessary. When you are satisfied that you have answered the questions to the best of your ability, transfer your answers to an answer sheet. Please refer to the information sheet that came with your course materials. Unit 2 Evaluation 188 MTHH 07136. Find the second derivative of the function f(x) = 8x9 . 4 a. f "(x) = -160 81 -13 b. f " ( x ) = 5 x 9 81 -13 c. f "(x) =. - -160 x 9 81 -13 d. f "(x) = 160 9 81 -13 e. f "(x) = 8x 9 37. Find the second derivative of the function f(x) = x sin x. a. f "(x) = 2 sin x + 2x cos x - x sin x b. f "(x) = 2 sin x + 4x cos x - x sin x c. f "(x) = sin x + 4x cos x - x sin x d. f "(x) = 2 sin x + 4x cos x - x sin x 38. The velocity of an object in meters per second is v(t) = 25 - f, 0 s ts 5. Find the acceleration of the object when t = 3. a. 3 meters per second squared b. -6 meters per second squared c. 6 meters per second squared d. -2 meters per second squared 39. Find the second derivative of the function f(x) = (3x5 + 7)'. a. f "(x) = 63x(7 + 3x) (14 + 63x) b. f " (x) = 63x(7 + 3x ) (14 + 60x) c. f "(x) = 63x(7 + 3x ) (14 + 60x ) d. f "(x) = 63x(7 + 3x ) (14 + 63x) e. f "(x) = 63x(7 + 3x ) (14 - 60x ) Unit 2 Evaluation 185 MTHH 071