Review Problems for Exam 2
(Covers chapter 3)
1.
Find the derivative of the function by the limit process.
a)
3
2
)
(
2
+

=
x
x
x
f
b)
1
)
(
+
=
x
x
f
2.
Find an equation of the line that is tangent to the graph of
)
7
)(
8
(
)
(
2
2


=
x
x
x
f
at (3, 2).
3.
Find the derivative of each of the following functions.
(a)
6
3
2
)
(
2
3
4

+

+
=
x
x
x
x
x
f
(b)
x
x
x
f
4
)
(
2

=
(c)
3
6
)
(
x
x
x
f

=
(d)
3
2
1
)
(


=
x
x
x
f
(e)
4
2
)
1
3
(
)
(
+

=
x
x
x
f
4.
Find an equation of the line that is tangent to the graph of
2
2
3
)
(
x
x
x
f
+

=
and
parallel to the line
3
2
4
=
+
y
x
.
5.
Find an equation of the line that is tangent to the graph of
2
3
)
(
x
x
f
+
=
and
perpendicular to the line
3
2
4
=
+
y
x
.
6.
If
5
3
2
)
(
2
+

+
=
x
x
x
x
f
, find
)
(
)
4
(
x
f
.
7.
A ball is thrown straight down from the top of a building. Its distance from the
ground is given by the position function
2
16
22
220
)
(
t
t
t
s


=
. Find its velocity
and acceleration after 3 seconds.
8.
Find the derivative of each of the following functions.
(a)
x
x
x
f
cos
sin
)
(
=
(b)
x
x
x
x
f
cos
sin
2
)
(
+
=
(c)
x
x
x
x
f
tan
2
)
(
2

=
(d)
x
x
y
cot
csc
+
=
(e)
3
1
)
(
x
x
f

=
(f)
6
2
1
)
5
(
)
5
2
(
)
(
x
x
x
x
f


=

(g)
)
1
3
(
sin
2
)
(
4
+
=
x
x
f
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 Fall '07
 PASCU
 Calculus, Derivative, 3 feet, 5 inches, 3 seconds, 3 centimeters

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