Practice Problems
Work through the odd-numbered problems 1-17. Once you have completed the problem set, check your answers.
Answers
1. (a) number of workers unemployed at time
.
and
.
(b) profit at time
.
and
.
(c) population at time
.
and
.
3. See Fig. 3.4P3.
Fig. 3.4P3.
5. (a) Concave up on . Concave down on
. (A small technical note: we have defined concavity only at points where the function is differentiable, so we exclude the endpoints and points where the function is not differentiable
from the intervals of concave up and concave down.)
7. .
.
so
is a local maximum.
so
is a local minimum.
9. .
so
is a local maximum.
so
is a local minimum.
and
changes concavity at
so
is an inflection point.
13. (a)
(b) at most
(c) at most .
15.
17. See Fig. 3.4P17.
Fig. 3.4P17.