Practice Problems
Work through the odd-numbered problems 1-21. Once you have completed the problem set, check your answers.
Answers
(b) Hypotenuse so
so
is increasing.
(c) Perimeter so
so
is increasing.
9. for all
so
and
so
and
When
and
, then
.
11. Let be the distance from the lamp post to the person, and
be the length of the shadow, both in feet. By similar triangles,
so
.
(The value of does not enter into the calculations).
(b) length of the string so
and
.
(3
. The volume is increasing at about
.
17. Given: with
constant. We also have
so
.
Therefore, so
. The radius
is changing at a constant rate.
For parts (b) and (c) we need to work in radians since our formulas for the derivatives of the trigonometric functions assume that the angles are measured in radians: radians so
radians
and
radians,
(The " - " indicates the distance to the sign is decreasing: you are approaching the sign). Your speed is
.