Practice Problems
Answers
1. See Fig. 3.3P1.
Fig. 3.3P1.
3. See Fig. 3.3P3.
Fig. 3.3P3.
5. See Fig. 3.3P5.
Fig. 3.3P5.
11. If is increasing then so and cannot both equal .
13. (a)
(b) maximum at
(c) none (or only at right endpoint)
15. Relative maximum height at . Relative minimum height at .
17. has a relative minimum at and a relative maximum at .
19. has a relative maximum at and relative minimums at and .
21. has a relative maximum at and no relative minimums.
23. No positive roots. is continuous. . Since for all , is increasing and never decreases back to the -axis (a root).
25. and . for all so is always increasing and can cross the -axis at most at one place. Since the graph of crosses the -axis at , that is the only root of .
27.
Fig. 3.3P27
29. (a) , , , or, in general, for any constant .
(b) for some value and so .
.
(c) $ for some value and so . .