MATH 1823
FINAL EXAMINATION - APRIL 1999 - ANSWERS
1. | (a) | y' = 6 x + x^{-1/2} - x^{-2} |
(b) | y' = 5 (4-x^{2})^{4} (-2 x) | |
(c) | y' = 2 x e^{x} + x^{2} e^{x} | |
(d) | ||
(e) | ||
(d) | ||
2. | (a) | 3 |
(b) | does not exist | |
(c) | 5/2 | |
3. | (a) | yes |
(b) | no | |
4. | (a) | |
(b) | y = -3 x | |
5. | (a) | |
(b) | 98/3 | |
(c) | ||
(d) | x e^{x} - e^{x} + C | |
(e) | 1/2 | |
6. | 7/3 | |
7. | 49,900 | |
8. | (a) | f'(x) = 4x^{3} - 16 x, f''(x) = 12 x^{2} - 16 |
(b) | increasing on (-2, 0) and (2, ), decreasing on (-, -2) and (0, 2) | |
(c) | concave up on ( ) and ( ), concave down on( ) | |
(d) | local max at (0, 16), local min at (-2, 0), local min at (2, 0) | |
(e) | inflection points at (-2/, 64/9) and (2/, 64/9) |