answers to end of chapter exerciseseco_mdb/corrections_to_eoc_answers.pdf · 7.162. 10 appendix a....

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















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


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




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


63. The percentage change in price is 62.3%, and the percentage changein quantity is 16.7%. 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




72. Price elasticity of demand is −0.25








80. The percentage change in the CPI was 4.9%





A.2. CHAPTER 2 5





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


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)


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


116. Not defined, you can not take the log of zero.




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


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





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.


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)



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





A.4. CHAPTER 4 13





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


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


3. On average the rate of change is 7.5 units of y per 1 unit of x











A.6. CHAPTER 6 15













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







34. The instantaneous rate of change is 1.5 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


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)


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)


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)


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.






















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


48. 17.5 feet and 17.5 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.

answers to end of chapter exerciseseco_mdb/corrections_to_eoc_answers.pdf · 7.162. 10 appendix a....

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