Homework 10/9
Identify each problem as type
I:
“Given location, find slope,”
II:
“Given slope, find location,” or
III:
“Find unknown constants.”
Then solve each problem.
1. An object is dropped from a tower so that after
t
seconds its height above ground is
h
(
t
) =
100

16
t
2
feet.
(a) What is its velocity after 2 seconds?
(b) When is its velocity

60 ft/s?
(c) What is its velocity at the time when it hits the ground?
(d) How high is it when its velocity is

48 ft/s?
2. The graph of
f
(
x
) = 1
/x
has a tangent
line that passes through (0
,
1
.
5) as shown
at right. Where is the point of tangency?
–1
–0.5
0
0.5
1
1.5
2
–1
1
2
3
4
x
3. Find the slope of the tangent to
y
= sin(2
x
) at the point
x
= 1.
4. Find one point on the graph of
y
= sin(2
x
) where the slope of the tangent line is 1.
5. Section 3.4; problems 32, 34, 35, 36. (No sketches or graphs required.)
6. The parabola
y
=
x
2
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 Fall '08
 STAFF
 Calculus, Slope, Velocity, 2 seconds, 0.2 m/s, 60 ft, 48 ft

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