Part 1:
|
1. B |
2. D |
3. E |
4. C |
5. D |
6. B |
7. E |
8. A |
9. E |
10. C |
|
11. A |
12. A |
13. C |
14. C |
15. E |
16. B |
17. C |
18. D |
19. D |
20. D |
Part 1:
|
1. D |
2. A |
3. E |
4. B |
5. C |
6. C |
7. D |
8. B |
9. E |
10. B* |
|
11. D |
12. D |
13. E |
14. A |
15. D |
16. B |
17. C |
18. B |
19. D |
20. B |
* Tangent line must cut the graph at the
x = 0, but there's a cusp at (0, f(0))
Part 2:
1. (a) s(t) = t3 - 15t2 + 48t - 24 (b) 0 < t < 2 or t > 8
(c) -6 ft/sec2 (d) v(5) = -27 ft/sec
(e)
|
t |
s(t) |
distance |
|
0 |
s(1) = -24 |
0 |
|
2 |
s(4) = 20 |
44 |
|
6 |
s(5) = -60 |
80 |
|
TOTAL DISTANCE: |
124 feet |
|
2, (a) f increases on (0, 6) since f’ is non-negative there
(c) f is concave down on (4, 5) since we can infer from the graph that f” is negative there
3. 1/6 ft/min
4. The 2 numbers are 10 and 10
Part 1:
|
1. B |
2. E |
3. C |
4. B |
5. C |
6. C |
7. D |
8. B |
9. E |
10. B |
|
11. B |
12. C |
13. D |
14. C |
15. D |
16. B |
17. A |
18. E |
19. B |
20. A |
Part 1:
|
1. C |
2. C |
3. C |
4. D |
5. D |
6. D |
7. E |
8. D |
9. A |
10. E |
|
11. B |
12. C |
13. D |
14. C |
15. B |
16. A |
17. B |
18. E |
19. A |
20. C |
Part 2:
1 (a) f increasing: 0 < x < 3 or x > 3
graph concave up:
-3 < x < 3
f’’ never = 0, therefore no inflection points
Vertical asymptotes: x = -3, x = 3
Horizontal asymptotes: y = 6
2. (a) x(t) = t3 - 5t2 - 8t + 32
(b) v(t) = 3t2 - 10t - 8, v(t) = (3t + 2)(t - 4) = 0. Therefore t = 4, (reject t = -2/3)
|
t |
x(t) |
distance |
|
1 |
x(1) = 20 |
0 |
|
4 |
x(4) = -16 |
36 |
|
5 |
x(5) = -8 |
8 |
|
TOTAL DISTANCE: |
44 feet |
|
3. (a) length = width = 2√(2)
3. (b) dx/dt = √(3)cm/sec (square root of 3)