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Appendix A
Answers to End of ChapterExercises
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, %∆Material = −51.8, %∆TotalCost =36.2, %∆NetIncome = 75.8
47. %∆Revenue = −89.5, %∆Labor = −59.3, %∆Material = −83.7,%∆TotalCost = −76.1, %∆NetIncome = −131.0
48. %∆Revenue = 64.5, %∆Labor = −89.6, %∆Material = −44.1,%∆TotalCost = −60.3, %∆NetIncome = 825.8
49. %∆Revenue = 7.2, %∆Labor = −32.1, %∆Material = 83.4, %∆TotalCost =19.2, %∆NetIncome = −7.7
50. %∆Revenue = 27.9, %∆Labor = 36.3, %∆Material = −86.3, %∆TotalCost =2.7, %∆NetIncome = 61.6
51. %∆Revenue = −6.0, %∆Labor = −35.4, %∆Material = 76.5, %∆TotalCost =37.1, %∆NetIncome = −139.9
52. %∆Revenue = 84.7, %∆Labor = 43.3, %∆Material = −19.5, %∆TotalCost =−13.4, %∆NetIncome = 188.9
53. %∆Revenue = −31.1, %∆Labor = −59.5, %∆Material = −5.4,%∆TotalCost = −47.1, %∆NetIncome = −11.1
54. %∆Revenue = −86.3, %∆Labor = 88.0, %∆Material = 75.7, %∆TotalCost =84.3, %∆NetIncome = −841.4
55. %∆Revenue = 82.0, %∆Labor = −56.7, %∆Material = −26.2,%∆TotalCost = −37.6, %∆NetIncome = 434.9
56. %∆Revenue = −17.5, %∆Labor = 63.3, %∆Material = −75.2,%∆TotalCost = 6.0, %∆NetIncome = −42.5
57. %∆Revenue = −68.5, %∆Labor = −56.9, %∆Material = 89.3,%∆TotalCost = −44.9, %∆NetIncome = −131.7
58. %∆Revenue = −82.4, %∆Labor = 21.5, %∆Material = 32.2, %∆TotalCost =26.5, %∆NetIncome = −203.2
59. %∆Revenue = −82.1, %∆Labor = −17.9, %∆Material = −20.4,%∆TotalCost = −18.4, %∆NetIncome = −182.8
60. %∆Revenue = −69.0, %∆Labor = 40.2, %∆Material = 89.3, %∆TotalCost =75.9, %∆NetIncome = −562.4
61. The percentage change in price is 84.1%, and the percentage changein quantity is 100.0%. The best deal is Brand B
62. The percentage change in price is 62.4%, and the percentage changein 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 changein quantity is 16.7%. The best deal is Brand A
64. The percentage change in price is 20.4%, and the percentage changein quantity is −54.5%. The best deal is Brand A
65. The percentage change in price is 85.4%, and the percentage changein quantity is 450.0%. The best deal is Brand B
66. The percentage change in price is 19.5%, and the percentage changein quantity is 200.0%. The best deal is Brand B
67. The percentage change in price is 20.8%, and the percentage changein quantity is −41.7%. The best deal is Brand A
68. The percentage change in price is 61.5%, and the percentage changein quantity is 0.0%. The best deal is Brand A
69. The percentage change in price is 60.1%, and the percentage changein quantity is 200.0%. The best deal is Brand B
70. The percentage change in price is 54.4%, and the percentage changein quantity is −50.0%. The best deal is Brand A
71. The percentage change in price is 15.0%, and the percentage changein 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 5
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
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. 1104
36. 132
37. 17
38. 1258
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
48.√
(5x− 2)3
49. 5√
45x2 + 5x− 9
A.2. CHAPTER 2 7
50.√x4(4− 3x2)4 = x2(4− 3x2)2
51. x2
52. 13x+5
53. 1
54. (8x− 9)2
55. 1x
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)
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(y2 + 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. 12 log(4x2 − 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 9
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 Chapter 3
1. 164
2. 328
3. 276
4. 84
5. 648
6. 576
7. 162
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 It2000 100.02001 110.02002 112.72003 123.8
15.
Year t It2001 100.02002 176.62003 248.52004 309.5
16.
Year t It2000 100.02001 140.52002 147.32003 254.2
17.
Year t It2004 100.02005 187.62006 322.52007 355.6
18.
Year t It2003 100.02004 184.52005 318.52006 571.5
19.
Year t It2003 100.02004 162.32005 203.72006 362.8
A.4. CHAPTER 4 11
20.
Year t It2003 100.02004 179.622005 305.352006 533.22
21.
Year t It2000 100.02001 151.492002 215.132003 337.596
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 itis 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 itis 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 15
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 ′(w) = 12w1
2. h′(z) = −4z−3
3. h′(x) = −63x8
4. g′(x) = 4.5x−0.75
16 APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
5. g′(z) = −5z−2
6. h′(z) = −2.25z−0.75
7. h′(w) = 1.0w−0.5
8. g′(z) = −16z7
9. f ′(x) = −9x8
10. g′(x) = 10x1
11. f ′(w) = −8w7
12. g′(x) = 12x3
13. f ′(x) = 14x−8
14. h′(x) = 60x5
15. g′(w) = 8w−2
16. h′(z) = 6z−7
17. f ′(z) = −60z−5
18. h′(z) = 64z3
19. g′(z) = 88z7
20. g′(z) = 24z−7
21. f ′(w) = −75w−6
22. g′(z) = 98z6
23. h′(z) = −63z8
24. f ′(w) = 40w−6
25. f ′(x) = 16x−5
26. g′(x) = −32x7
27. h′(x) = −140x−11
28. g′(x) = −99x−10
29. h′(x) = 15
30. f ′(x) = −90x−10
31. h′(x) = 96x7 + 81x8
32. h′(z) = −105z−8
A.6. CHAPTER 6 17
33. f ′(w) = −135w−10
34. h′(z) = −8
35. f ′(w) = −51w−4
36. g′(x) = 2.0x−0.5 − 13x−2 − 3x2
37. f ′(x) = −60x−7
38. h′(x) = −15x−4 − 40x3
39. g′(w) = −30w5 + 36w3 − 24w7
40. f ′(w) = −60w5 − 68w−5
41. g′(z) = 63z6 + 16z7 − 8z−5
42. h′(x) = −15x−4 − 112x−9
43. g′(x) = 32x7 − 33x−4
44. f ′(x) = 90x8 − 25x−6 + 4.0x−0.5
45. f ′(z) = −70z−11 + 50z−11
46. g′(x) = 63x8
47. h′(w) = 24w1 + 4w−5
48. g′(z) = −152z−9 − 18z−2
49. h′(x) = 6
50. h′(w) = 72w8 − 49w−8
51. f ′(x) = (55x4)(−8x−2) + (11x5 + 928)(16x−3)
52. g′(z) = (8.0z−0.5+27z−4)(10z4+16z−3−3z2+88)+(16z0.5−9z−3)(40z3−48z−4 − 6z1)
53. f ′(x) = (75x4)(−7x6 − 179) + (15x5)(−42x5)
54. g′(x) = (28x−5 + 18x−4 − 14x−3)(−2x + 7x3 + 6x9 + 13) + (−7x−4 −6x−3 + 7x−2)(−2 + 21x2 + 54x8)
55. f ′(w) = (2w−2)(5w−3 + 11w−10 + 7w−8) + (−2w−1 − 80)(−15w−4 −110w−11 − 56w−9)
56. h′(x) = (−36x−10 − 136x−9)(−4x−9 + 7x−7 − 3x−6) + (4x−9 + 17x−8 −169)(36x−10 − 49x−8 + 18x−7)
57. g′(w) = (−112w−8 + 136w7)(6w) + (16w−7 + 17w8 + 673)(6)
18 APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
58. f ′(z) = (−8z7 − 19z−2)(3z3 + 3z0.75) + (−1z8 + 19z−1 − 95)(9z2 +2.25z−0.25)
59. f ′(z) = (16z7)(−4z9 + 5z6 − 136) + (2z8)(−36z8 + 30z5)
60. h′(z) = (3.0z−0.5 + 36z2 − 30z−7)(7z5 − 3z7) + (6z0.5 + 12z3 + 5z−6 −840)(35z4 − 21z6)
61. g′(z) = (30z−6)(11z−9 + 17z2 + 19z6) + (−6z−5 + 17)(−99z−10 + 34z1 +114z5)
62. f ′(z) = (119z6 − 48z−9 + 50z4)(15z2) + (17z7 + 6z−8 + 10z5)(30z1)
63. f ′(x) = (−54x−7 − 36x8 − 54x8)(−7x0.25 − 8x−7 + 97) + (9x−6 − 4x9 −6x9 − 375)(−1.75x−0.75 + 56x−8)
64. f ′(w) = (70w−11 + 6w−4)(−10w3 + 12w8 − 3w−1 + 454) + (−7w−10 −2w−3)(−30w2 + 96w7 + 3w−2)
65. h′(x) = (−56x−5)(19x−5 + 11x0.5) + (14x−4)(−95x−6 + 5.5x−0.5)
66. g′(w) = (−56w−9 + 85w4 + 7.5w−0.25)(−4w−4− 4w5) + (7w−8 + 17w5 +10w0.75 − 419)(16w−5 − 20w4)
67. f ′(x) = (26x1)(16x6 + 14x3 + 9x−1− 815) + (13x2)(96x5 + 42x2− 9x−2)
68. f ′(z) = (32z−9 +16−8z−5)(−7z−6−3z3 +7z−6 +783)+(−4z−8 +16z +2z−4)(42z−7 − 9z2 − 42z−7)
69. f ′(z) = (27z8 + 0.2z−0.9)(13z−6 − 879) + (3z9 + 2z0.1 − 440)(−78z−7)
70. h′(z) = (−36z−4−54z5)(−8z2−5z5+7z0.5)+(12z−3−9z6−308)(−16z1−25z4 + 3.5z−0.5)
71. h′(x) = (5x−2+60x−7)(2x7)−(−5x−1−10x−6)(14x6)(2x7)2
72. h′(w) = (108w5+7w6)(6w−8+15w−4+103)−(18w6+w7)(−48w−9−60w−5)(6w−8+15w−4+103)2
73. g′(x) = (112x7+10x1+24x2)(13x2+174)−(14x8+5x2+8x3)(26x1)(13x2+174)2
74. f ′(z) = (6z−4−0.3z−0.9)(12z0.25)−(−2z−3−3z0.1+80)(3.0z−0.75)(12z0.25)2
75. g′(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. h′(w) = (−20w−11)(−6w−3+7w−1)−(2w−10)(18w−4−7w−2)(−6w−3+7w−1)2
77. f ′(x) = (−21x2+153x8)(−6x7−5x0.1+440)−(−7x3+17x9)(−42x6−0.5x−0.9)(−6x7−5x0.1+440)2
78. h′(w) = (10w4)(7w−3−233)−(2w5)(−21w−4)(7w−3−233)2
A.6. CHAPTER 6 19
79. g′(z) = (−12z−2−24z−5+9z−10)(13z7+10z6)−(12z−1+6z−4−1z−9)(91z6+60z5)(13z7+10z6)2
80. h′(w) = (−85w−6+70w−11−50w−6)(−3w)−(17w−5−7w−10+10w−5)(−3)(−3w)2
81. f ′(w) = (54w−10)(−5w−2+591)−(−6w−9−101)(10w−3)(−5w−2+591)2
82. f ′(w) = (80w−9)(−5w4−6w6+802)−(−10w−8)(−20w3−36w5)(−5w4−6w6+802)2
83. g′(z) = (75z4)(6z−6+13z4−411)−(15z5+926)(−36z−7+52z3)(6z−6+13z4−411)2
84. g′(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′(w) = (20w4)(−4w+10w3+691)−(4w5)(−4+30w2)(−4w+10w3+691)2
86. h′(x) = (2.25x−0.25+13−40x−5)(x5−881)−(3x0.75+13x+10x−4)(5x4)(x5−881)2
87. g′(z) = (100z−11)(18z0.1+13z−3)−(−10z−10+106)(1.8z−0.9−39z−4)(18z0.1+13z−3)2
88. h′(z) = (42z6−20z−5)(−4z−9z5)−(6z7+5z−4)(−4−45z4)(−4z−9z5)2
89. f ′(x) = (3−18x−2)(9x−10+13x2+16x−6)−(3x+18x−1)(−90x−11+26x1−96x−7)(9x−10+13x2+16x−6)2
90. h′(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 ′(x) = −24(10x−4 − 9x−4 + 821)−2(−40x−5 + 36x−5)
92. f ′(w) = 108(5w + 15w4)3(5 + 60w3)
93. f ′(z) = −31.0(14z3 − 3z9 + 4z−7 + 551)−1.5(42z2 − 27z8 − 28z−8)
94. g′(x) = −117(5x−2)8(−10x−3)
95. h′(z) = 320(z6)3(6z5)
96. h′(x) = 180(5x−7 + 11x0.1 + 5x−3 − 169)8(−35x−8 + 1.1x−0.9 − 15x−4)
97. f ′(x) = −36(2x0.25 − 2x−9 − 577)2(0.5x−0.75 + 18x−10)
98. h′(z) = 81(−2z−4 − 2z8 − 8z5)−4(8z−5 − 16z7 − 40z4)
99. g′(x) = −234(5x−7 + 918)−10(−35x−8)
100. h′(z) = −75(4z)2(4)
101. g′(w) = −268(14w9 + 8w−3 − 8w8 − 279)−5(126w8 − 24w−4 − 64w7)
102. g′(w) = 420(16w6 + 5w−2)4(96w5 − 10w−3)
103. f ′(x) = −162(−8x3 + 2x−7 + 452)5(−24x2 − 14x−8)
20 APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
104. g′(x) = 38(10x3 − 3x−2)1(30x2 + 6x−3)
105. h′(w) = −378(13w−10)−8(−130w−11)
106. g′(z) = 215(−9z−3 + 3z−4 − 272)4(27z−4 − 12z−5)
107. g′(w) = 190(2w7 − 727)1(14w6)
108. g′(z) = 828(−1z−8 + 15z7 + 10z5)8(8z−9 + 105z6 + 50z4)
109. g′(w) = 7(3w9 + 17w−5 + 3w9 + 718)6(27w8 − 85w−6 + 27w8)
110. h′(w) = 234(4w3 + 14w0.1)2(12w2 + 1.4w−0.9)
111. g′(x) = 81 (2.0x−0.5−36x−7+18x2)(4x0.5+6x−6+6x3)
112. h′(x) = −8 (−42x−4)(14x−3+383)
113. f ′(x) = 73 (−52x−5−16x3)(13x−4−4x4−937)
114. g′(z) = 63 (−60z−5−16z−9)(15z−4+2z−8)
115. g′(x) = 74 (40x3)(10x4)
116. g′(w) = 51 (16w7+1.7w−0.9)(2w8+17w0.1)
117. g′(w) = 1 (42w−7+45w8)(−7w−6+5w9−514)
118. f ′(x) = 6 (45x8+3x2)(5x9+x3−781)
119. g′(z) = −23 (100z−11+36z1+16)(−10z−10+18z2+16z)
120. f ′(w) = 52 (21w6−7w−8−72w8)(3w7+w−7−8w9−560)
121. f ′(x) = 17 (34x1−99x−10)(17x2+11x−9)
122. f ′(w) = −17 (8w−5+2−27w−4)(−2w−4+2w+9w−3)
123. g′(z) = −7 (−24z−7−63z−8)(4z−6+9z−7+713)
124. f ′(w) = 10 (2)(2w+277)
125. h′(x) = −20 (4)(4x)
126. f ′(w) = 58 (8w1+63w8+128w7)(4w2+7w9+16w8−754)
127. g′(x) = −19 (39x2−54x8−35x−6)(13x3−6x9+7x−5+317)
A.6. CHAPTER 6 21
128. h′(w) = −13 (30w2−42w−7)(10w3+7w−6+539)
129. h′(w) = 50 (10w4)(2w5−325)
130. f ′(w) = 69 (−63w8−14w6−50w4)(−7w9−2w7−10w5)
131. h′(w) = (21w6) ln(4.28) 983(4.28)(3w7)
132. h′(z) = (54z−10 + 4z3 + 0.7z−0.9) ln(1.42) 764(1.42)(−6z−9+z4+7z0.1−349)
133. h′(x) = (−16x−9) ln(6.49) 464(6.49)(2x−8)
134. f ′(x) = (6x−3 + 35x−8 − 21x2) ln(7.38) 812(7.38)(−3x−2−5x−7−7x3+371)
135. h′(x) = (−40x7 − 57x−4) ln(8.91) 193(8.91)(−5x8+19x−3)
136. h′(z) = (−25z−6) ln(5.95) 785(5.95)(5z−5−748)
137. h′(x) = (−63x−8) ln(2.47) 912(2.47)(9x−7)
138. h′(w) = (80w−11) ln(2.05) 400(2.05)(−8w−10+196)
139. f ′(x) = (120x7 + 5x4 − 104x−9) ln(9.16) 868(9.16)(15x8+x5+13x−8−117)
140. g′(w) = (−81w8 − 55w−6) ln(4.45) 24(4.45)(−9w9+11w−5)
141. h′(z) = (133z6 − 30z5) ln(1.62) 541(1.62)(19z7−5z6)
142. g′(x) = (2.5x−0.75 − 152x−9) ln(3.52) 476(3.52)(10x0.25+19x−8−981)
143. h′(w) = (49w−8) ln(9.87) 948(9.87)(−7w−7−48)
144. f ′(w) = (−36w−7) ln(8.34) 925(8.34)(6w−6)
145. g′(z) = (112z6 − 66z−7 + 12z−7) ln(3.69) 684(3.69)(16z7+11z−6−2z−6)
146. g′(w) = (−28w−3 − 2w−2 − 4) ln(4.02) 123(4.02)(14w−2+2w−1−4w−257)
147. g′(x) = (−40x−9−180x−11+5x−6) ln(0.76) 827(0.76)(5x−8+18x−10−1x−5+476)
148. g′(z) = (24z5) ln(3.27) 538(3.27)(4z6)
149. g′(w) = (12w1) ln(2.98) 983(2.98)(6w2−573)
150. f ′(x) = (−80x7) ln(8.1) 722(8.1)(−10x8+496)
22 APPENDIX A. ANSWERS TO END OF CHAPTER EXERCISES
A.7 Chapter 7
1. h′(x) = 24x2−672x+2760, maximum at x = 5 and minimum at x = 23.
2. h′(z) = 30z2−870z+1620, maximum at x = 2 and minimum at x = 27.
3. f ′(w) = −30w2 + 1680w− 23490, minimum at x = 27 and maximum atx = 29.
4. g′(z) = 18z2 − 108z + 90, maximum at x = 1 and minimum at x = 5.
5. f ′(w) = −6w2 − 216w − 1794, minimum at x = 13 and maximum atx = 23.
6. f ′(z) = −30z2 + 900z − 3750, maximum at x = 25 and minimum atx = 5.
7. g′(z) = 24z2−960z+9384, maximum at x = 17 and minimum at x = 23.
8. f ′(x) = −6x2 − 246x − 2400, minimum at x = 16 and maximum atx = 25.
9. h′(w) = −24w2 − 840w − 7296, maximum at x = 19 and minimum atx = 16.
10. h′(w) = −12w2 + 468w − 4320, maximum at x = 24 and minimum atx = 15.
11. f ′(z) = 30z2−1050z+6480, maximum at x = 8 and minimum at x = 27.
12. h′(w) = 30w2 − 1170w + 10500, maximum at x = 14 and minimum atx = 25.
13. g′(w) = 24w2 − 1200w + 14784, maximum at x = 22 and minimum atx = 28.
14. f ′(z) = −12z2 − 396z − 2760, maximum at x = 23 and minimum atx = 10.
15. h′(z) = −6z2−138z−792, maximum at x = 12 and minimum at x = 11.
16. h′(z) = 6z2−288z+3432, maximum at x = 22 and minimum at x = 26.
17. g′(w) = 6w2−192w+1242, maximum at x = 9 and minimum at x = 23.
18. f ′(x) = −6x2 − 270x − 2784, maximum at x = 29 and minimum atx = 16.
19. g′(x) = −18x2 − 342x − 1260, maximum at x = 14 and minimum atx = 5.
A.7. CHAPTER 7 23
20. h′(x) = −30x2 − 930x − 1740, minimum at x = 2 and maximum atx = 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 ofthe two lengths is a minimum. The relationship between the two lengthsis a concave down parabola product = x(L − x) = Lx − x2. A 40 footrope could be split into a 39.999 foot length and a 0.001 length with aresulting product of 0.039999 sq. ft. But it could also be split into a39.9999 foot lenth and a 0.0001 foot length with a resulting product of0.0039999, which is even smaller.