4-1 Answers - WordPress.com · 04/08/2016 · 4-5 Answers 1. Make Sure You Understand! 2. Make Sure...
Transcript of 4-1 Answers - WordPress.com · 04/08/2016 · 4-5 Answers 1. Make Sure You Understand! 2. Make Sure...
Unit 4 Answers
4-1 Answers
1. 3
2. (5,−2)
3. x = 0, 4, 5
4. x = 1
5. CN: x = 32
6. CN: x = 0, 8
7. CN: None
8. CN: x = −2
9. abs. max.: 10 abs. min.: −94
10. abs. max.: 8 abs. min.: 0
11. abs. max.: 4 abs. min.: 0
12. abs. max.: 2 abs. min.: 0
13. abs. max.: 2 abs. min.: 0
14. abs. max.: −3 abs. min.: −15
15. abs. max.: 23 abs. min.: 0
16. abs. max.: 3 abs. min.: 0
17. abs. max.: none abs. min.: 0
18. abs. max.: none abs. min.: 0
19. abs. max.: 2 abs. min.: 0
20. MVT Does Not Apply
21. MVT Does Apply; c = 2
22. MVT Does Apply; c = 32
23. MVT Does Not Apply
24. MVT Does Apply; c = 827
25. MVT Does Not Apply
26. MVT Does Not Apply
27. MVT Does Apply; c = 1
28. c = −.215, 1.548 (or 1.549)
29. c = 2.414
30. (a) vavg = −48 ft/sec on [0, 3]
(b) t = 1.5 sec
4-2 Answers
1. (a) (−∞,−2), (2,∞)
(b) (−2, 2)
(c) rel. min. (2,−4)
(d) rel. max. (−2, 4)
2. (a) (−∞,−2), (0,∞)
(b) (−2,−1), (−1, 0)
(c) rel. min. (0, 0)
(d) rel. max. (−2,−4)
3. (a) (−2, 0), (2,∞)
(b) (−∞,−2), (0, 2)
(c) rel. min. (±2, 0)
(d) rel. max. (0, 4)
4. (a) (0,∞)
(b) (−∞, 0)
(c) rel. min. (0, 0)
(d) no rel. max.
5. (a) (−∞,−2), (0,∞)
(b) (−2, 0)
(c) rel. min. x = 0
(d) rel. max. x = −2
6. (a) (−2, 0), (3,∞)
(b) (−∞,−2), (0, 3)
(c) rel. min. x = −2, 3
(d) no rel. max.
7. Problem 2
8. Problem 3
9. (a) (4,∞)
(b) (−∞, 4)
(c) rel. min. (4,−16)
(d) no rel. max.
10. (a) (−∞, 1)
(b) (1,∞)
(c) no rel. min.
(d) rel. max. (1, 8)
11. (a) (−∞,−2), (1,∞)
(b) (−2, 1)
(c) rel. min. (1,−7)
(d) rel. max. (−2, 20)
12. (a) (−∞, 0), (1,∞)
(b) (0, 1)
(c) rel. min.(1, 1
10
)(d) rel. max. (0, 1)
13. (a) (−∞,∞)
(b) never
(c) no rel. min.
(d) no rel. max.
14. (a) never
(b) (∞,−3), (−3, 3), (3,∞)
(c) no rel. min.
(d) no rel. max.
15. (a) (−1,∞)
(b) (−∞,−1)
(c) rel. min. (−1, 0)
(d) no rel. max.
16. (a) (−∞,−1), (−1,∞)
(b) never
(c) no rel. min.
(d) no rel. max.
17. (a)(32 ,∞
)(b)
(−∞, 3
2
)(c) rel. min.
(32 ,−2716
)(d) no rel. max.
18. Yes
19. Yes
20. No
21. 0 ≤ t < 2 sec
22. 70 ft
23. (a) Never
(b) t > 2 sec
24. a = −4, b = 0
25. abs. max.: 73 abs. min.: −7
26. abs. max.: 4 abs. min.: 2
27. CN: all reals
28. MVT can not be used
29. c = −.333
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4-3 Answers
1. (a) (−∞, 1)
(b) (1,∞)
(c) (1, 0)
2. (a) (−2, 2)
(b) (−∞,−2), (2,∞)
(c) none
3. (a) (−∞,−1), (0, 1)
(b) (−1, 0), (1,∞)
(c) (−1,−1), (0, 0), (1, 1)
4. (a) (−2, 1), (4, 6), (8, 9)
(b) (6, 8)
(c) (6, 1)
5. (a) (−∞, 0), (2,∞)
(b) (0, 2)
(c) (0, 2), (2,−14)
6. (a) (1,∞)
(b) (−∞, 1)
(c) (1,−2)
7. (a) never
(b) (−∞, 0), (0,∞)
(c) none
8. rel. max.: (0, 6) rel. min.: (2, 2)
9. rel. max.:(±3, 101
4
)rel. min.: (0, 5)
10. rel. max: at x = −3 rel. min.: at x = 3
11. rel. max: at x = 0 rel. min.: at x = −2, 4
12. Show your work!
13. Show your work!
14. Show your work!
15. Concave Down
16. abs. max.: 8 abs. min.: −1
17. c = 3
18. d = 2, b = 0, a = 1, c = −3
19. (a) Picture!
(b) Picture!
(c) Picture!
(d) Picture!
20. (a)dy
dx= 0
(b) y′′ = −1
(c) rel. max. at (1,−2)
21. g′(4) < 0
22. g′(4) > 0
23. g′(4) > 0
24. (a) t > 0
(b) −3 < t < 0, t > 3
(c) t > 3.644
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4-4 Answers
1. Graph!
2. Graph!
3. Graph!
4. Graph!
5. Graph!
6. Graph!
7. Graph!
8. Graph!
9. Graph!
10. False
11. Removable: x = 2 Nonremovable: x = 1
12. Removable: none Nonremovable: x = 0
13. Removable: none Nonremovable: multiples of 3
14. 14
15. DNE
16. 0
17. y − 64 = 88.722(x− 5) [or y − 64 = 88.723(x− 5)]
18. (a) (0,−3), (0, 1)
(b) rel. min.: (0,−3) rel. max.: (0, 1)
19. (±√
8,−1)
20. B
21. C
22. A
23. D
24. (a) m = −23
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(b) m = −23
(c) m = 0
(d) m undefined
(e) m ≈ −1
(f) m = 0
(g) m ≈ 1
(h) m ≈ 3
(i) m ≈ −1
(j) m = 0
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4-5 Answers
1. Make Sure You Understand!
2. Make Sure You Understand!
3. Make Sure You Understand!
4. Make Sure You Understand!
5. Make Sure You Understand!
6. Make Sure You Understand!
7. Make Sure You Understand!
8. Make Sure You Understand!
9. Make Sure You Understand! The Graph of f couldbe shifted vertically.
10. Make Sure You Understand!
11. Make Sure You Understand!
12. Make Sure You Understand!
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13. Make Sure You Understand!
14. rel. max.: (0,−5) rel. min.:(2,−9)
15. Make Sure You Understand!
16. c =√
43
17. abs. max.: 14 abs. min.: −18
18. Let y = −x2 − 6x. Then:
19. c = 16 b = −12 a = 2
20. loc. min. at x = 3
21. loc. max. at x = 3
22. False. [Find a counterexample!]
23. True
24. False. [Find a counterexample!]
25. True
26. False. [Find a counterexample!]
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