Exam 3 Review – MAC 2233
*
This is intended to be a tool to help you review some of the material that could appear on the
exam. It is not inclusive of all topics discussed in lecture.
1. Graph
f
(
x
) = (
x

1)
1
3
(
x
+ 2)
2
3
.
Note:
f
0
(
x
) =
x
(
x

1)
2
3
(
x
+ 2)
1
3
and
f
00
(
x
) =

2
(
x

1)
5
3
(
x
+ 2)
4
3
2. The graph of
f
0
(
x
)
is given. Give a possible sketch of
f
(
x
)
if
f
is known to be continuous.
3. Find the particular function
E
(
t
) =
Ae

bt
(where
A
and
b
are constants) with
E
intercept 4 and
such that
E
(1) =
e
. What is E(2) ?
4. Find the asymptotes of the function
f
(
x
) =
2
x
2

8
6

x

x
2
; evaluate
lim
x
→
3
+
f
(
x
)
.
5. Sketch the graph of
f
(
x
) = ln(
x

4) + 2
. Write its inverse function and evaluate
lim
x
→
4
+
f
(
x
)
.
6. Find the domain and asymptotes for each of the following functions:
f
(
x
) = ln(2
x

x
2
)
g
(
x
) =
e
x
2
e
x

4
h
(
x
) =
4
1 + ln(
x
)
7. Solve these equations for
x
:
(a)
ln(2
x

5)

ln(
x

2) = 0
(b)
5(12

2
x
2
) = 20
8. If
f
(
x
)
has horizontal tangent lines at
x
=

2
,
x
= 1
,
x
= 5
, and if
f
00
(
x
)
has the following
signs, find the relative extrema of
f
(
x
)
.
9. On which interval(s) is
f
(
x
) = (
x
2
+ 1)
e
x
concave up? concave down? Find all points of inflec
tion. Sketch the graph.
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 Spring '08
 Smith
 Calculus, Derivative, $1, #, $2, $2.50

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