Appendix A
Answers to End of Chapter
Exercises
Modified 9-1-2011
A.1
Chapter 1
1. 33.5%
2. 123.0%
3. 76.6%
4. 232.0%
5. 1121.1%
6. 11.1%
7. 45.5%
8. 105.3%
9. 161.9%
10. 145.8%
11. 175.6%
12. 65.6%
13. 51.1%
14. 67.9%
15. 59.9%
16. Labor % = 57.4, Material % = 14.7, Administrative % = 27.9
1
2
APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
17. Labor % = 89.2, Material % = 8.9, Administrative % = 1.9
18. Labor % = 78.2, Material % = 17.8, Administrative % = 4.0
19. Labor % = 58.6, Material % = 22.6, Administrative % = 18.8
20. Labor % = 77.1, Material % = 13.0, Administrative % = 9.9
21. Labor % = 31.5, Material % = 64.0, Administrative % = 4.5
22. Labor % = 38.0, Material % = 10.7, Administrative % = 51.3
23. Labor % = 57.2, Material % = 37.5, Administrative % = 5.3
24. Labor % = 94.6, Material % = 5.0, Administrative % = 0.4
25. Labor % = 65.4, Material % = 32.0, Administrative % = 2.6
26. Labor % = 22.9, Material % = 18.8, Administrative % = 58.3
27. Labor % = 33.7, Material % = 19.5, Administrative % = 46.8
28. Labor % = 45.2, Material % = 50.7, Administrative % = 4.1
29. Labor % = 27.1, Material % = 4.9, Administrative % = 68.0
30. Labor % = 90.8, Material % = 3.6, Administrative % = 5.6
31. 25.424%
32. -46.429%
33. 300.000%
34. 566.667%
35. 95.556%
36. 0.0%
37. -45.000%
38. -13.095%
39. 310.000%
40. -27.500%
41. -45.455%
42. -41.975%
43. -18.519%
44. 3.922%
A.1. CHAPTER 1
3
45. 200.000%
46. %∆Revenue = 49.2, %∆Labor = 76.3, %∆M aterial = −51.8, %∆T otalCost =
36.2, %∆N etIncome = 75.8
47. %∆Revenue = −89.5, %∆Labor = −59.3, %∆M aterial = −83.7,
%∆T otalCost = −76.1, %∆N etIncome = −131.0
48. %∆Revenue = 64.5, %∆Labor = −89.6, %∆M aterial = −44.1,
%∆T otalCost = −60.3, %∆N etIncome = 825.8
49. %∆Revenue = 7.2, %∆Labor = −32.1, %∆M aterial = 83.4, %∆T otalCost =
19.2, %∆N etIncome = −7.7
50. %∆Revenue = 27.9, %∆Labor = 36.3, %∆M aterial = −86.3, %∆T otalCost =
2.7, %∆N etIncome = 61.6
51. %∆Revenue = −6.0, %∆Labor = −35.4, %∆M aterial = 76.5, %∆T otalCost =
37.1, %∆N etIncome = −139.9
52. %∆Revenue = 84.7, %∆Labor = 43.3, %∆M aterial = −19.5, %∆T otalCost =
−13.4, %∆N etIncome = 188.9
53. %∆Revenue = −31.1, %∆Labor = −59.5, %∆M aterial = −5.4,
%∆T otalCost = −47.1, %∆N etIncome = −11.1
54. %∆Revenue = −86.3, %∆Labor = 88.0, %∆M aterial = 75.7, %∆T otalCost =
84.3, %∆N etIncome = −841.4
55. %∆Revenue = 82.0, %∆Labor = −56.7, %∆M aterial = −26.2,
%∆T otalCost = −37.6, %∆N etIncome = 434.9
56. %∆Revenue = −17.5, %∆Labor = 63.3, %∆M aterial = −75.2,
%∆T otalCost = 6.0, %∆N etIncome = −42.5
57. %∆Revenue = −68.5, %∆Labor = −56.9, %∆M aterial = 89.3,
%∆T otalCost = −44.9, %∆N etIncome = −131.7
58. %∆Revenue = −82.4, %∆Labor = 21.5, %∆M aterial = 32.2, %∆T otalCost =
26.5, %∆N etIncome = −203.2
59. %∆Revenue = −82.1, %∆Labor = −17.9, %∆M aterial = −20.4,
%∆T otalCost = −18.4, %∆N etIncome = −182.8
60. %∆Revenue = −69.0, %∆Labor = 40.2, %∆M aterial = 89.3, %∆T otalCost =
75.9, %∆N etIncome = −562.4
61. The percentage change in price is 84.1%, and the percentage change
in quantity is 100.0%. The best deal is Brand B
62. The percentage change in price is 62.4%, and the percentage change
in quantity is −12.5%. The best deal is Brand A
4
APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
63. The percentage change in price is 62.3%, and the percentage change
in quantity is 16.7%. The best deal is Brand A
64. The percentage change in price is 20.4%, and the percentage change
in quantity is −54.5%. The best deal is Brand A
65. The percentage change in price is 85.4%, and the percentage change
in quantity is 450.0%. The best deal is Brand B
66. The percentage change in price is 19.5%, and the percentage change
in quantity is 200.0%. The best deal is Brand B
67. The percentage change in price is 20.8%, and the percentage change
in quantity is −41.7%. The best deal is Brand A
68. The percentage change in price is 61.5%, and the percentage change
in quantity is 0.0%. The best deal is Brand A
69. The percentage change in price is 60.1%, and the percentage change
in quantity is 200.0%. The best deal is Brand B
70. The percentage change in price is 54.4%, and the percentage change
in quantity is −50.0%. The best deal is Brand A
71. The percentage change in price is 15.0%, and the percentage change
in quantity is 42.9%. The best deal is Brand B
72. Price elasticity of demand is −0.25
73. Price elasticity of demand is −0.67
74. Price elasticity of demand is −1.50
75. Price elasticity of demand is −4.00
76. Price elasticity of demand is −0.11
77. Price elasticity of demand is −0.25
78. Price elasticity of demand is −1.00
79. Price elasticity of demand is −1.50
80. The percentage change in the CPI was 4.9%
81. The percentage change in the CPI was 8.1%
82. The percentage change in the CPI was 12.5%
83. The percentage change in the CPI was 3.8%
84. The percentage change in the CPI was 1.1%
A.2. CHAPTER 2
85. The percentage change in the CPI was 6.1%
86. The percentage change in the CPI was 2.9%
87. The percentage change in the CPI was 2.7%
88. The percentage change in the CPI was 1.6%
A.2
Chapter 2
1. 215
2. 310
3. 411
4. 810
5. 810
6. 1012
7. (3x − 4)8
8. (2x3 − 4)8
9. (5x)9
10. 4(3x − 4)11
11. 100(6x2 + 14)4
12. 212
13. 43
14. 56
15. (x − 2)2
16. (3x + 2)4
17. (4x2 − 2)4
18. 108
19. 1015
20. 36
21. 521
22. 76
5
6
APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
23. (x − 3)8
24. (3x2 − 2)20
25. (2x5 − 3x)30
26. (4x3 − 3x2 )10
27. (7x2 − 2x + 5)24
28. 1
29. 1
30. 1
31. 1
32. 1
33. 1
34. 1
35.
1
104
36.
1
32
37.
1
7
38.
1
258
39.
1
(6x2 +3x−5)2
40.
1
(4x+3)4
41.
1
(65x+2)6
42. 4x + 5
√
43.
64 = 8
√
44.
121 = 11
√
45. 3 512 = 8
√
46.
5x − 2
√
47. 4 15x3 − 2x2 + 6x − 15
p
48.
(5x − 2)3
√
49. 5 45x2 + 5x − 9
A.2. CHAPTER 2
50.
p
x4 (4 − 3x2 )4 = x2 (4 − 3x2 )2
51. x2
52.
1
3x+5
53. 1
54. (8x − 9)2
55.
1
x
56. 4x2 − 5
57. 10y−x
58. 1
59. log3 (9) = 2
60. log2 (16) = 4
61. log10 (10, 000) = 4
62. log5 (25) = 2
63. log4 (64) = 3
64. log5 (125) = 3
65. log100 (10, 000) = 2
66. log2.718 (20.079290232) = 3
67. 27 = 33
68. 625 = 54
69. 3, 125 = 55
70. 1, 953, 125 = 59
71. 2, 187 = 37
72. 81 = 34
73. 243 = 35
74. 15, 625 = 56
75. 75 = 53
76. log(10) + log(x2 + 5)
77. log(3x − 4) + log(5x + 5)
7
8
APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
78. log(6x2 − 4x + 5) + log(2x2 + 7x + 8)
79. log(25) + log(−x2 + 4x + 90)
80. 2log(x) + 2log(y)
81. log(x3 − 45) + log(y 2 + 6)
82. log(x2 − 6) − log(5x + 6)
83. Not defined, you can not take the log of a negative number.
84. 2log(x) − log(8)
85. log(3x2 + 76) − log(35x + 26)
86. log(3) + 2log(x) − log(5) − log(y)
87. log(2x3 − 7) − log(15y + 6)
88. 7log(4x2 − 3)
89.
1
2
2 log(4x
− 3)
90. −4log(4x2 − 3)
91. 6log(x)
92. log(x)
93. 3log(x5 − 30)
94. 1
95. 1
96. 1
97. 1
98. 7
99. 4
100. 7
101. 4
102. 7
103. 4
104. 100
105. 25
A.3. CHAPTER 3
106. 100
107. 27
108. 100 − 3x
109. 5x + 3
110. 0
111. 0
112. 0
113. 0
114. 0
115. Not defined, you can not take the log of a negative number.
116. Not defined, you can not take the log of zero.
117. Not defined, you can not take the log of a negative number.
118. Not defined, you can not take the log of a negative number.
119. Not defined, you can not take the log of a negative number.
120. 2log(x) + 3log(y) − 4log(w)
121. xlog(2) + ylog(4)
122. xlog(100) + ylog(1, 000) = 2x + 3y
123. 2x
124. ln(5) + 2ln(x) − ln(z)
A.3
1. 164
2. 328
3. 276
4. 84
5. 648
6. 576
7. 162
Chapter 3
9
10
APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
8. 1,326
9. 1,262
10. 26,244
11. 2
12. 324
13. 324
14.
Year t
2000
2001
2002
2003
It
100.0
110.0
112.7
123.8
15.
Year t
2001
2002
2003
2004
It
100.0
176.6
248.5
309.5
16.
Year t
2000
2001
2002
2003
It
100.0
140.5
147.3
254.2
17.
Year t
2004
2005
2006
2007
It
100.0
187.6
322.5
355.6
18.
Year t
2003
2004
2005
2006
It
100.0
184.5
318.5
571.5
19.
Year t
2003
2004
2005
2006
It
100.0
162.3
203.7
362.8
A.4. CHAPTER 4
20.
Year t
2003
2004
2005
2006
It
100.0
179.62
305.35
533.22
21.
Year t
2000
2001
2002
2003
It
100.0
151.49
215.13
337.596
11
22. I2010 = 71.5
23. I2005 = 114.5
24. I2001 = 86.1
25. I2010 = 103.0
26. I2010 = 93.6
27. I2005 = 118.8
28. I2001 = 90.6
29. I2010 = 103.4
30. $392.20 in year 2006 dollars, cheaper in 1986
31. $530.98 in year 2007 dollars, cheaper in 2007
32. $594.99 in year 2000 dollars, cheaper in 2000
33. $524.70 in year 2008 dollars, cheaper in 2008
34. $592.62 in year 2005 dollars, cheaper in 2005
A.4
Chapter 4
1. y = 2x + 10
2. y = −2x + 10
3. y = −1x + 20
4. y = x + 15
5. y = 3x + 100
6. Ca = 55 + .03x and Cb = 50 + .05x. If you talk less than 250 minutes it
is cheaper to use company B.
12
APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
7. Ca = 35 + .10x and Cb = 40 + .05x. If you drive less than 100 miles it
is cheaper to use company A.
8. q = −2p + 100
9. q = −4p + 80
10. q = −4p + 80
11. q = −1.5p + 30
12. vertex at (1, 0.5)
13. vertex at (2, 1)
14. vertex at (2, −0.5)
15. vertex at (−2, 1.75)
16. vertex at (4, −10)
17. horizontal (x axis) intercepts (1, 0) and (3, 0)
18. horizontal (x axis) intercepts (1, 0) and (5, 0)
19. horizontal (x axis) intercepts (2, 0) and (6, 0)
20. horizontal (x axis) intercepts (−6, 0) and (10, 0)
21. exponential growth
22. exponential decay
23. exponential decay
24. exponential growth
25. The optimal quantity is 15.5121 units. Revenue = $5036.68 Total Cost
= $984.21
26. The optimal quantity is 4.6863 units. Revenue = $603.64 Total Cost =
$141.30
27. The optimal quantity is 2.2261 units. Revenue = $255.68 Total Cost =
$164.52
28. The optimal quantity is 14.1423 units. Revenue = $9866.06 Total Cost
= $3093.75
29. The optimal quantity is 13.8616 units. Revenue = $5889.78 Total Cost
= $2373.63
30. The optimal quantity is 5.9519 units. Revenue = $2143.39 Total Cost
= $665.97
A.4. CHAPTER 4
13
31. The optimal quantity is 6.3147 units. Revenue = $668.21 Total Cost =
$375.02
32. The optimal quantity is 9.9393 units. Revenue = $621.89 Total Cost =
$294.45
33. The optimal quantity is 3.6228 units. Revenue = $440.88 Total Cost =
$361.70
34. The optimal quantity is 16.1499 units. Revenue = $5420.06 Total Cost
= $650.40
35. y = 5.33333(1.22474)x
36. y = 2.50(1.25992)x
37. y = 16(0.50)x
38. y = 45.25483(0.50)x
39. y = 0.01426(9.00)x
40. y = 0.01646(3.00)x
41. y = 4.00(1.43450)x
42. $12,915.48
43. $12,994.32
44. $13,001.76
45. $8,954.24
46. $10,650.72
47. $4,730.72
48. $541.43
49. $239,392.05
50. $228,193.47
51. $176,172.02
52. $18,098.25
53. $9,425.96
54. $10,643.05
55. $27,173.42
14
APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
56. $4,708.88
57. 79.033061271543 years
58. 76.9445590209697 years
59. 76.7528364331349 years
60. 67.1374002256011 years
61. 65.363248886745 years
62. 65.2003834238024 years
63. 59.8376804420107 years
64. 57.7562969212991 years
65. 57.5646273248511 years
66. 50.8312121000101 years
67. 49.0631080154059 years
68. 48.9002875678518 years
A.5
Chapter 5
1. On average the rate of change is 12 units of y per 1 unit of x
2. On average the rate of change is 9 units of y per 1 unit of x
3. On average the rate of change is 7.5 units of y per 1 unit of x
4. On average the rate of change is 6.75 units of y per 1 unit of x
5. On average the rate of change is 6.375 units of y per 1 unit of x
6. On average the rate of change is 6.1875 units of y per 1 unit of x
7. On average the rate of change is 6.09375 units of y per 1 unit of x
8. On average the rate of change is 6.04688 units of y per 1 unit of x
9. On average the rate of change is 6.02344 units of y per 1 unit of x
10. On average the rate of change is 15 units of y per 1 unit of x
11. On average the rate of change is 13.5 units of y per 1 unit of x
12. On average the rate of change is 12.75 units of y per 1 unit of x
13. On average the rate of change is 12.375 units of y per 1 unit of x
A.6. CHAPTER 6
14. On average the rate of change is 12.1875 units of y per 1 unit of x
15. On average the rate of change is 12.0938 units of y per 1 unit of x
16. On average the rate of change is 12.0469 units of y per 1 unit of x
17. On average the rate of change is 12.0234 units of y per 1 unit of x
18. On average the rate of change is 27 units of y per 1 unit of x
19. On average the rate of change is 25.5 units of y per 1 unit of x
20. On average the rate of change is 24.75 units of y per 1 unit of x
21. On average the rate of change is 24.375 units of y per 1 unit of x
22. On average the rate of change is 24.1875 units of y per 1 unit of x
23. On average the rate of change is 24.0938 units of y per 1 unit of x
24. On average the rate of change is 24.0469 units of y per 1 unit of x
25. On average the rate of change is 24.0234 units of y per 1 unit of x
26. The instantaneous rate of change is 6 units of y per unit of x
27. The instantaneous rate of change is −2 units of y per unit of x
28. The instantaneous rate of change is 2 units of y per unit of x
29. The instantaneous rate of change is −6 units of y per unit of x
30. The instantaneous rate of change is −1 units of y per unit of x
31. The instantaneous rate of change is 12 units of y per unit of x
32. The instantaneous rate of change is 2 units of y per unit of x
33. The instantaneous rate of change is −1 units of y per unit of x
34. The instantaneous rate of change is 1.5 units of y per unit of x
35. The instantaneous rate of change is 12 units of y per unit of x
A.6
Chapter 6
1. f 0 (w) = 12w1
2. h0 (z) = −4z −3
3. h0 (x) = −63x8
4. g 0 (x) = 4.5x−0.75
15
16
APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
5. g 0 (z) = −5z −2
6. h0 (z) = −2.25z −0.75
7. h0 (w) = 1.0w−0.5
8. g 0 (z) = −16z 7
9. f 0 (x) = −9x8
10. g 0 (x) = 10x1
11. f 0 (w) = −8w7
12. g 0 (x) = 12x3
13. f 0 (x) = 14x−8
14. h0 (x) = 60x5
15. g 0 (w) = 8w−2
16. h0 (z) = 6z −7
17. f 0 (z) = −60z −5
18. h0 (z) = 64z 3
19. g 0 (z) = 88z 7
20. g 0 (z) = 24z −7
21. f 0 (w) = −75w−6
22. g 0 (z) = 98z 6
23. h0 (z) = −63z 8
24. f 0 (w) = 40w−6
25. f 0 (x) = 16x−5
26. g 0 (x) = −32x7
27. h0 (x) = −140x−11
28. g 0 (x) = −99x−10
29. h0 (x) = 15
30. f 0 (x) = −90x−10
31. h0 (x) = 96x7 + 81x8
32. h0 (z) = −105z −8
A.6. CHAPTER 6
17
33. f 0 (w) = −135w−10
34. h0 (z) = −8
35. f 0 (w) = −51w−4
36. g 0 (x) = 2.0x−0.5 − 13x−2 − 3x2
37. f 0 (x) = −60x−7
38. h0 (x) = −15x−4 − 40x3
39. g 0 (w) = −30w5 + 36w3 − 24w7
40. f 0 (w) = −60w5 − 68w−5
41. g 0 (z) = 63z 6 + 16z 7 − 8z −5
42. h0 (x) = −15x−4 − 112x−9
43. g 0 (x) = 32x7 − 33x−4
44. f 0 (x) = 90x8 − 25x−6 + 4.0x−0.5
45. f 0 (z) = −70z −11 + 50z −11
46. g 0 (x) = 63x8
47. h0 (w) = 24w1 + 4w−5
48. g 0 (z) = −152z −9 − 18z −2
49. h0 (x) = 6
50. h0 (w) = 72w8 − 49w−8
51. f 0 (x) = (55x4 )(−8x−2 ) + (11x5 + 928)(16x−3 )
52. g 0 (z) = (8.0z −0.5 +27z −4 )(10z 4 +16z −3 −3z 2 +88)+(16z 0.5 −9z −3 )(40z 3 −
48z −4 − 6z 1 )
53. f 0 (x) = (75x4 )(−7x6 − 179) + (15x5 )(−42x5 )
54. g 0 (x) = (28x−5 + 18x−4 − 14x−3 )(−2x + 7x3 + 6x9 + 13) + (−7x−4 −
6x−3 + 7x−2 )(−2 + 21x2 + 54x8 )
55. f 0 (w) = (2w−2 )(5w−3 + 11w−10 + 7w−8 ) + (−2w−1 − 80)(−15w−4 −
110w−11 − 56w−9 )
56. h0 (x) = (−36x−10 − 136x−9 )(−4x−9 + 7x−7 − 3x−6 ) + (4x−9 + 17x−8 −
169)(36x−10 − 49x−8 + 18x−7 )
57. g 0 (w) = (−112w−8 + 136w7 )(6w) + (16w−7 + 17w8 + 673)(6)
18
APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
58. f 0 (z) = (−8z 7 − 19z −2 )(3z 3 + 3z 0.75 ) + (−1z 8 + 19z −1 − 95)(9z 2 +
2.25z −0.25 )
59. f 0 (z) = (16z 7 )(−4z 9 + 5z 6 − 136) + (2z 8 )(−36z 8 + 30z 5 )
60. h0 (z) = (3.0z −0.5 + 36z 2 − 30z −7 )(7z 5 − 3z 7 ) + (6z 0.5 + 12z 3 + 5z −6 −
840)(35z 4 − 21z 6 )
61. g 0 (z) = (30z −6 )(11z −9 + 17z 2 + 19z 6 ) + (−6z −5 + 17)(−99z −10 + 34z 1 +
114z 5 )
62. f 0 (z) = (119z 6 − 48z −9 + 50z 4 )(15z 2 ) + (17z 7 + 6z −8 + 10z 5 )(30z 1 )
63. f 0 (x) = (−54x−7 − 36x8 − 54x8 )(−7x0.25 − 8x−7 + 97) + (9x−6 − 4x9 −
6x9 − 375)(−1.75x−0.75 + 56x−8 )
64. f 0 (w) = (70w−11 + 6w−4 )(−10w3 + 12w8 − 3w−1 + 454) + (−7w−10 −
2w−3 )(−30w2 + 96w7 + 3w−2 )
65. h0 (x) = (−56x−5 )(19x−5 + 11x0.5 ) + (14x−4 )(−95x−6 + 5.5x−0.5 )
66. g 0 (w) = (−56w−9 + 85w4 + 7.5w−0.25 )(−4w−4 − 4w5 ) + (7w−8 + 17w5 +
10w0.75 − 419)(16w−5 − 20w4 )
67. f 0 (x) = (26x1 )(16x6 + 14x3 + 9x−1 − 815) + (13x2 )(96x5 + 42x2 − 9x−2 )
68. f 0 (z) = (32z −9 + 16 − 8z −5 )(−7z −6 − 3z 3 + 7z −6 + 783) + (−4z −8 + 16z +
2z −4 )(42z −7 − 9z 2 − 42z −7 )
69. f 0 (z) = (27z 8 + 0.2z −0.9 )(13z −6 − 879) + (3z 9 + 2z 0.1 − 440)(−78z −7 )
70. h0 (z) = (−36z −4 −54z 5 )(−8z 2 −5z 5 +7z 0.5 )+(12z −3 −9z 6 −308)(−16z 1 −
25z 4 + 3.5z −0.5 )
71. h0 (x) =
(5x−2 +60x−7 )(2x7 )−(−5x−1 −10x−6 )(14x6 )
(2x7 )2
72. h0 (w) =
(108w5 +7w6 )(6w−8 +15w−4 +103)−(18w6 +w7 )(−48w−9 −60w−5 )
(6w−8 +15w−4 +103)2
73. g 0 (x) =
(112x7 +10x1 +24x2 )(13x2 +174)−(14x8 +5x2 +8x3 )(26x1 )
(13x2 +174)2
74. f 0 (z) =
(6z −4 −0.3z −0.9 )(12z 0.25 )−(−2z −3 −3z 0.1 +80)(3.0z −0.75 )
(12z 0.25 )2
75. g 0 (w) =
(40w3 +81w−10 )(4w−4 +2w−2 +12w−5 )−(10w4 −9w−9 +969)(−16w−5 −4w−3 −60w−6 )
(4w−4 +2w−2 +12w−5 )2
76. h0 (w) =
(−20w−11 )(−6w−3 +7w−1 )−(2w−10 )(18w−4 −7w−2 )
(−6w−3 +7w−1 )2
77. f 0 (x) =
(−21x2 +153x8 )(−6x7 −5x0.1 +440)−(−7x3 +17x9 )(−42x6 −0.5x−0.9 )
(−6x7 −5x0.1 +440)2
78. h0 (w) =
(10w4 )(7w−3 −233)−(2w5 )(−21w−4 )
(7w−3 −233)2
A.6. CHAPTER 6
79. g 0 (z) =
(−12z −2 −24z −5 +9z −10 )(13z 7 +10z 6 )−(12z −1 +6z −4 −1z −9 )(91z 6 +60z 5 )
(13z 7 +10z 6 )2
80. h0 (w) =
(−85w−6 +70w−11 −50w−6 )(−3w)−(17w−5 −7w−10 +10w−5 )(−3)
(−3w)2
81. f 0 (w) =
(54w−10 )(−5w−2 +591)−(−6w−9 −101)(10w−3 )
(−5w−2 +591)2
82. f 0 (w) =
(80w−9 )(−5w4 −6w6 +802)−(−10w−8 )(−20w3 −36w5 )
(−5w4 −6w6 +802)2
83. g 0 (z) =
19
(75z 4 )(6z −6 +13z 4 −411)−(15z 5 +926)(−36z −7 +52z 3 )
(6z −6 +13z 4 −411)2
84. g 0 (w) =
(−20w−3 +100w−11 +20w−6 )(13w−1 +7w−1 )−(10w−2 −10w−10 −4w−5 )(−13w−2 −7w−2 )
(13w−1 +7w−1 )2
85. g 0 (w) =
(20w4 )(−4w+10w3 +691)−(4w5 )(−4+30w2 )
(−4w+10w3 +691)2
86. h0 (x) =
(2.25x−0.25 +13−40x−5 )(x5 −881)−(3x0.75 +13x+10x−4 )(5x4 )
(x5 −881)2
87. g 0 (z) =
(100z −11 )(18z 0.1 +13z −3 )−(−10z −10 +106)(1.8z −0.9 −39z −4 )
(18z 0.1 +13z −3 )2
88. h0 (z) =
(42z 6 −20z −5 )(−4z −9z 5 )−(6z 7 +5z −4 )(−4−45z 4 )
(−4z −9z 5 )2
89. f 0 (x) =
(3−18x−2 )(9x−10 +13x2 +16x−6 )−(3x+18x−1 )(−90x−11 +26x1 −96x−7 )
(9x−10 +13x2 +16x−6 )2
90. h0 (x) =
(−0.75x−0.25 )(7x0.1 +17x5 +5x−7 )−(−1x0.75 )(0.7x−0.9 +85x4 −35x−8 )
(7x0.1 +17x5 +5x−7 )2
91. f 0 (x) = −24(10x−4 − 9x−4 + 821)−2 (−40x−5 + 36x−5 )
92. f 0 (w) = 108(5w + 15w4 )3 (5 + 60w3 )
93. f 0 (z) = −31.0(14z 3 − 3z 9 + 4z −7 + 551)−1.5 (42z 2 − 27z 8 − 28z −8 )
94. g 0 (x) = −117(5x−2 )8 (−10x−3 )
95. h0 (z) = 320(z 6 )3 (6z 5 )
96. h0 (x) = 180(5x−7 + 11x0.1 + 5x−3 − 169)8 (−35x−8 + 1.1x−0.9 − 15x−4 )
97. f 0 (x) = −36(2x0.25 − 2x−9 − 577)2 (0.5x−0.75 + 18x−10 )
98. h0 (z) = 81(−2z −4 − 2z 8 − 8z 5 )−4 (8z −5 − 16z 7 − 40z 4 )
99. g 0 (x) = −234(5x−7 + 918)−10 (−35x−8 )
100. h0 (z) = −75(4z)2 (4)
101. g 0 (w) = −268(14w9 + 8w−3 − 8w8 − 279)−5 (126w8 − 24w−4 − 64w7 )
102. g 0 (w) = 420(16w6 + 5w−2 )4 (96w5 − 10w−3 )
103. f 0 (x) = −162(−8x3 + 2x−7 + 452)5 (−24x2 − 14x−8 )
20
APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
104. g 0 (x) = 38(10x3 − 3x−2 )1 (30x2 + 6x−3 )
105. h0 (w) = −378(13w−10 )−8 (−130w−11 )
106. g 0 (z) = 215(−9z −3 + 3z −4 − 272)4 (27z −4 − 12z −5 )
107. g 0 (w) = 190(2w7 − 727)1 (14w6 )
108. g 0 (z) = 828(−1z −8 + 15z 7 + 10z 5 )8 (8z −9 + 105z 6 + 50z 4 )
109. g 0 (w) = 7(3w9 + 17w−5 + 3w9 + 718)6 (27w8 − 85w−6 + 27w8 )
110. h0 (w) = 234(4w3 + 14w0.1 )2 (12w2 + 1.4w−0.9 )
−0.5
−7
−36x +18x
111. g 0 (x) = 81 (2.0x
(4x0.5 +6x−6 +6x3 )
2)
−4
(−42x )
112. h0 (x) = −8 (14x
−3 +383)
−5
3
(−52x −16x )
113. f 0 (x) = 73 (13x
−4 −4x4 −937)
−5
−9
−16z )
114. g 0 (z) = 63 (−60z
(15z −4 +2z −8 )
3
(40x )
115. g 0 (x) = 74 (10x
4)
−0.9
7
+1.7w
)
116. g 0 (w) = 51 (16w
(2w8 +17w0.1 )
−7
8
(42w +45w )
117. g 0 (w) = 1 (−7w
−6 +5w 9 −514)
8
2
(45x +3x )
118. f 0 (x) = 6 (5x
9 +x3 −781)
−11
1
(100z
+36z +16)
119. g 0 (z) = −23 (−10z
−10 +18z 2 +16z )
−8
6
8
(21w −7w −72w )
120. f 0 (w) = 52 (3w
7 +w −7 −8w 9 −560)
−10
1
−99x
)
121. f 0 (x) = 17 (34x
(17x2 +11x−9 )
−5
−4
(8w +2−27w )
122. f 0 (w) = −17 (−2w
−4 +2w+9w −3 )
−7
−8
(−24z −63z )
123. g 0 (z) = −7 (4z
−6 +9z −7 +713)
(2)
124. f 0 (w) = 10 (2w+277)
(4)
125. h0 (x) = −20 (4x)
1
8
7
(8w +63w +128w )
126. f 0 (w) = 58 (4w
2 +7w 9 +16w 8 −754)
2
8
−6
(39x −54x −35x )
127. g 0 (x) = −19 (13x
3 −6x9 +7x−5 +317)
A.6. CHAPTER 6
21
−7
2
(30w −42w )
128. h0 (w) = −13 (10w
3 +7w −6 +539)
4
(10w )
129. h0 (w) = 50 (2w
5 −325)
8
6
4
−14w −50w )
130. f 0 (w) = 69 (−63w
(−7w9 −2w7 −10w5 )
131. h0 (w) = (21w6 ) ln(4.28) 983(4.28)(3w
7)
132. h0 (z) = (54z −10 + 4z 3 + 0.7z −0.9 ) ln(1.42) 764(1.42)(−6z
133. h0 (x) = (−16x−9 ) ln(6.49) 464(6.49)(2x
−8 )
134. f 0 (x) = (6x−3 + 35x−8 − 21x2 ) ln(7.38) 812(7.38)(−3x
135. h0 (x) = (−40x7 − 57x−4 ) ln(8.91) 193(8.91)(−5x
136. h0 (z) = (−25z −6 ) ln(5.95) 785(5.95)(5z
−9 +z 4 +7z 0.1 −349)
−2 −5x−7 −7x3 +371)
8 +19x−3 )
−5 −748)
137. h0 (x) = (−63x−8 ) ln(2.47) 912(2.47)(9x
−7 )
138. h0 (w) = (80w−11 ) ln(2.05) 400(2.05)(−8w
−10 +196)
139. f 0 (x) = (120x7 + 5x4 − 104x−9 ) ln(9.16) 868(9.16)(15x
140. g 0 (w) = (−81w8 − 55w−6 ) ln(4.45) 24(4.45)(−9w
141. h0 (z) = (133z 6 − 30z 5 ) ln(1.62) 541(1.62)(19z
8 +x5 +13x−8 −117)
9 +11w −5 )
7 −5z 6 )
0.25 +19x−8 −981)
142. g 0 (x) = (2.5x−0.75 − 152x−9 ) ln(3.52) 476(3.52)(10x
143. h0 (w) = (49w−8 ) ln(9.87) 948(9.87)(−7w
−7 −48)
144. f 0 (w) = (−36w−7 ) ln(8.34) 925(8.34)(6w
−6 )
145. g 0 (z) = (112z 6 − 66z −7 + 12z −7 ) ln(3.69) 684(3.69)(16z
146. g 0 (w) = (−28w−3 − 2w−2 − 4) ln(4.02) 123(4.02)(14w
7 +11z −6 −2z −6 )
−2 +2w −1 −4w−257)
147. g 0 (x) = (−40x−9 −180x−11 +5x−6 ) ln(0.76) 827(0.76)(5x
148. g 0 (z) = (24z 5 ) ln(3.27) 538(3.27)(4z
6)
149. g 0 (w) = (12w1 ) ln(2.98) 983(2.98)(6w
2 −573)
150. f 0 (x) = (−80x7 ) ln(8.1) 722(8.1)(−10x
8 +496)
−8 +18x−10 −1x−5 +476)
22
A.7
APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
Chapter 7
1. h0 (x) = 24x2 −672x+2760, maximum at x = 5 and minimum at x = 23.
2. h0 (z) = 30z 2 − 870z + 1620, maximum at x = 2 and minimum at x = 27.
3. f 0 (w) = −30w2 + 1680w − 23490, minimum at x = 27 and maximum at
x = 29.
4. g 0 (z) = 18z 2 − 108z + 90, maximum at x = 1 and minimum at x = 5.
5. f 0 (w) = −6w2 − 216w − 1794, minimum at x = 13 and maximum at
x = 23.
6. f 0 (z) = −30z 2 + 900z − 3750, maximum at x = 25 and minimum at
x = 5.
7. g 0 (z) = 24z 2 −960z +9384, maximum at x = 17 and minimum at x = 23.
8. f 0 (x) = −6x2 − 246x − 2400, minimum at x = 16 and maximum at
x = 25.
9. h0 (w) = −24w2 − 840w − 7296, maximum at x = 19 and minimum at
x = 16.
10. h0 (w) = −12w2 + 468w − 4320, maximum at x = 24 and minimum at
x = 15.
11. f 0 (z) = 30z 2 −1050z+6480, maximum at x = 8 and minimum at x = 27.
12. h0 (w) = 30w2 − 1170w + 10500, maximum at x = 14 and minimum at
x = 25.
13. g 0 (w) = 24w2 − 1200w + 14784, maximum at x = 22 and minimum at
x = 28.
14. f 0 (z) = −12z 2 − 396z − 2760, maximum at x = 23 and minimum at
x = 10.
15. h0 (z) = −6z 2 −138z −792, maximum at x = 12 and minimum at x = 11.
16. h0 (z) = 6z 2 − 288z + 3432, maximum at x = 22 and minimum at x = 26.
17. g 0 (w) = 6w2 − 192w + 1242, maximum at x = 9 and minimum at x = 23.
18. f 0 (x) = −6x2 − 270x − 2784, maximum at x = 29 and minimum at
x = 16.
19. g 0 (x) = −18x2 − 342x − 1260, maximum at x = 14 and minimum at
x = 5.
A.7. CHAPTER 7
23
20. h0 (x) = −30x2 − 930x − 1740, minimum at x = 2 and maximum at
x = 29.
21. The optimal quantity is 1.5169 units. Revenue = $130.03 Total Cost =
$116.55
22. The optimal quantity is 21.4672 units. Revenue = $15554.52 Total Cost
= $6627.44
23. The optimal quantity is 15.491 units. Revenue = $7980.95 Total Cost
= $2448.66
24. The optimal quantity is 5.8012 units. Revenue = $936.14 Total Cost =
$469.26
25. The optimal quantity is 6.207 units. Revenue = $637.19 Total Cost =
$289.14
26. The optimal quantity is 1.4605 units. Revenue = $79.22 Total Cost =
$91.22
27. The optimal quantity is 3.5871 units. Revenue = $511.17 Total Cost =
$258.86
28. The optimal quantity is 7.8017 units. Revenue = $1586.7 Total Cost =
$724.81
29. The optimal quantity is 21.4353 units. Revenue = $7300.48 Total Cost
= $3293.66
30. The optimal quantity is 19.2495 units. Revenue = $11142.86 Total Cost
= $3828.65
31. The optimal quantity is 1.6406 units. Revenue = $104.43 Total Cost =
$186.57
32. The optimal quantity is 19.8731 units. Revenue = $16326.97 Total Cost
= $7153.46
33. The optimal quantity is 11.9332 units. Revenue = $5030.43 Total Cost
= $742.91
34. The optimal quantity is 9.4332 units. Revenue = $4515.72 Total Cost
= $1275.37
35. The optimal quantity is 3.8446 units. Revenue = $439.55 Total Cost =
$352.24
36. The optimal quantity is 30.1256 units. Revenue = $21264.47 Total Cost
= $9138.59
24
APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
37. The optimal quantity is 55.2487 units. Revenue = $26669.99 Total Cost
= $9367.32
38. The optimal quantity is 10.7022 units. Revenue = $5005.64 Total Cost
= $1294.78
39. The optimal quantity is 2.5833 units. Revenue = $198.13 Total Cost =
$187.91
40. The optimal quantity is 11.981 units. Revenue = $8492.48 Total Cost
= $2739.76
41. 40.0250 feet by 20.0125 feet
42. 32.1870 feet by 16.0935 feet
43. 31.6860 feet by 15.8430 feet
44. 30.0666 feet by 15.0333 feet
45. 24.2899 feet by 12.1450 feet
46. 25 feet and 25 feet
47. 12 feet and 12 feet
48. 17.5 feet and 17.5 feet
49. 21 feet and 21 feet
50. 30 feet and 30 feet
51. It is not possible to divide a rope of any length L so that the product of
the two lengths is a minimum. The relationship between the two lengths
is a concave down parabola product = x(L − x) = Lx − x2 . A 40 foot
rope could be split into a 39.999 foot length and a 0.001 length with a
resulting product of 0.039999 sq. ft. But it could also be split into a
39.9999 foot lenth and a 0.0001 foot length with a resulting product of
0.0039999, which is even smaller.