A-17 Answers to Selected Exercises 3.4 Exercises 1. A 3. one 5. B and D 7. ƒ1x2 = x1x + 5221x - 32 9. x y 2 0 1 f(x) = 2x4 (a) 10, ∞2 (b) 1-∞, 02 11. x y 4 2 –2 0 f(x) = – x2 5 3 (a) none (b) 1-∞, ∞2 13. x y 4 2 –2 0 f(x) = x3 + 1 1 2 (a) 1-∞, ∞2 (b) none 15. x y 8 2 0 f(x) = –(x + 1)3 + 1 (a) none (b) 1-∞, ∞2 29. x y –4 –2 1 2 0 –8 f(x) = x3 + 5x2 + 2x – 8 31. x 0 1 2 –3 –1 8 16 –8 f(x) = –2x(x – 3)(x + 2) y 17. x y 2 8 0 f(x) = (x – 1)4 + 2 (a) 11, ∞2 (b) 1-∞, 12 19. x y 4 6 0 2 f(x) = (x – 2)2 + 4 1 2 (a) 12, ∞2 (b) 1-∞, 22 37. x 0 2 –6 10 –10 –20 –30 20 f(x) = x3 + 5x2 – x – 5 y 39. x 0 –1 1 3 3 –3 f(x) = –x3 + x2 + 2x y 41. x y 4 –16 –32 0 1 f(x) = 2x3(x2 – 4)(x – 1) 43. –4 –2 2 4 –30 10 20 f(x) = 2x3 – 5x2 – x + 6 0 x y 21. 23. 25. 27. 33. x 0 4 2 –24 f(x) = x2(x – 2)(x + 3)2 y –16 –3 35. x 0 1 –3 5 –10 f(x) = (3x – 1)(x + 2)2 y 45. –2–5 1 2 5 15 20 0 f(x) = 3x4 – 7x3 – 6x2 + 12x + 8 y x 47. ƒ122 = -2 60; ƒ132 = 1 70 49. ƒ102 = -7 60; ƒ112 = 1 70 51. ƒ112 = -6 60; ƒ122 = 16 70 53. ƒ13.22 = -3.8144 60; ƒ13.32 = 7.1891 70 55. ƒ1-12 = -35 60; ƒ102 = 12 70 65. ƒ1x2 = 1 2 1x + 621x - 221x - 52, or ƒ1x2 = 1 2 x 3 - 1 2 x 2 - 16x + 30 67. ƒ1x2 = 1x - 1231x + 123, or ƒ1x2 = x6 - 3x4 + 3x2 - 1 69. ƒ1x2 = 1x - 3221x + 322, or ƒ1x2 = x4 - 18x2 + 81 71. f(x) = –2x(x – 3)(x + 2) −12 −3 20 4 ƒ11.252 = 14.21875 73. f(x) = (3x – 1)(x + 2)2 −15 −4 15 2 ƒ11.252 = 29.046875 75. 2.7807764 77. 1.543689 79. -3.0, -1.4, 1.4 81. -1.1, 1.2 83. 1-0.09, 1.052 85. 11.76, -5.342 87. 1-3.44, 26.152 89. Answers will vary. 91. (a) 0 6x 66 (b) V1x2 = x118 - 2x2112 - 2x2, or V1x2 = 4x3 - 60x2 + 216x (c) x ≈2.35; 228.16 in.3 (d) 0.42 6x 65 93. (a) x - 1; 11, ∞2 (b) 2x2 - 1x - 122 (c) 2x3 - 5x2 + 4x - 28,225 = 0 (d) hypotenuse: 25 in.; legs: 24 in. and 7 in. 95. 3 ft 97. (a) 7.13 cm; The ball floats partly above the surface. (b) The sphere is more dense than water and sinks below the surface. (c) 10 cm; The balloon is submerged with its top even with the surface. 99. (a) 500 15 3000 75 (b) y = 33.93x + 113.4 500 15 3000 75 (c) y = −0.0032x3 + 0.4245x2 + 16.64x + 323.1 500 15 3000 75 (d) linear: 1572 ft; cubic: 1569 ft (e) The cubic function is a slightly better fit because only one data point is not on the curve. 101. B
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