Answer Key
819
67 . 3− 1
; error, ~4.632×10 −7
600
69 . dy = (cos x − x sin x ) dx 71 . dy = ⎛ ⎝ ⎜ x 2 −2 x −2 ( x −1) 2 ⎞ ⎠ ⎟ dx
73 . dy = − 1
dx , − 1 16
( x +1) 2
x 2 +12 x −2 2( x +1) 3/2 ⎛ ⎝ 3 x 2 +2− 1 x 2
75 . dy = 9
dx , −0.1 ⎞ ⎠ dx , 0.2
77 . dy =
79 . 12 xdx 81 . 4 πr 2 dr 83 . −1.2 π cm 3 85 . −100 ft 3
91 . Answers may vary 93 . Answers will vary 95 . No; answers will vary 97 . Since the absolute maximum is the function (output) value rather than the x value, the answer is no; answers will vary 99 .When a =0 101 . Absolute minimum at 3; Absolute maximum at −2.2; local minima at −2, 1; local maxima at −1, 2 103 . Absolute minima at −2, 2; absolute maxima at −2.5, 2.5; local minimum at 0; local maxima at −1, 1
105 . Answers may vary. 107 . Answers may vary. 109 . x =1 111 . None 113 . x =0 115 . None 117 . x =−1, 1 119 . Absolute maximum: x =4, y = 33
x =1, y =3
2 ; absolute minimum:
121 . Absolute minimum: x = 1 2 , y =4 123 . Absolute maximum: x =2 π , y =2 π ; absolute minimum: x =0, y =0 125 . Absolute maximum: x =−3; absolute minimum: −1≤ x ≤1, y =2 127 . Absolute maximum: x = π 4 , y = 2; absolute minimum: x = 5 π 4 , y =− 2 129 . Absolute minimum: x =−2, y =1 131 . Absolute minimum: x =−3, y =−135; local maximum: x =0, y =0; local minimum: x =1, y =−7 133 . Local maximum: x =1−2 2, y =3−4 2; local minimum: x =1+2 2, y =3+4 2 135 . Absolute maximum: x = 2 2 , y = 3 2 ; absolute minimum: x = − 2 2 , y = − 3 2
137 . Local maximum: x =−2, y =59; local minimum: x =1, y =−130 139 . Absolute maximum: x =0, y =1; absolute minimum: x =−2, 2, y =0 141 . h = 9245 49 m, t = 300 49 s 143 . The global minimum was in 1848, when no gold was produced. 145 . Absolute minima: x =0, x =2, y =1; local maximum at x =1, y =2 147 . No maxima/minima if a is odd, minimum at x =1 if a is even 149 . One example is f ( x ) = | x | +3, −2≤ x ≤2 151 . Yes, but the Mean Value Theorem still does not apply
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