MATH 1823
FINAL EXAMINATION - APRIL 1998 - ANSWERS
1. | (a) | (i) , (ii) |
(b) | (i) 1, (ii) 3/2 | |
2. | (a) | (i) , (ii) |
(b) | y' = 6x + 6 | |
(c) | (not covered in course) | |
3. | (a) | |
(b) | ||
(c) | ||
(d) | ||
(e) | (not covered in course) | |
(f) | ||
4. | (a) | x^{3} + 8 x^{-1/2} + C |
(b) | ||
(c) | ||
(d) | ||
(e) | ||
(f) | 27 | |
5. | (a) | f'(x) = 3 x^{2} + 3x -6, f''(x) = 6x + 3 |
(b) | increasing on (, -2) and (1, ), decreasing on (-2, 1) | |
(c) | concave up on (-1/2, ), concave down on (, -1/2) | |
(d) | critical points: (-2, 14) and (1, -1/3) | |
(e) | x = -2 gives a local maximum | |
(f) | x = 1 gives a local minimum | |
(g) | inflection point at ( ) | |
6. | (b) | y = 4x+1 |
(c) | 4/3 | |
7. | (a) | abs max: 1/2, abs min: 2/5 |
(b) | 1/2 | |
(c) | 901/20 |