Chapter 4 Test
October 27, 2008
Name
1. Find the x

coordinate
H
s
L
of the absolute maximum of
f
H
x
L
=
3x
4

4x
3
+
12x
2
+
2
Justify your answer.
2. f
H
x
L
=
x
1
ÄÄÄ
3
H
2

x
L
Find all critical values from
the
second
derivative
for this function
H
x

values only, and these would be potential points of inflection
L
.
3. f
H
x
L
=
sinx cosx
Use the Second Derivative Test to find all local extreme values
H
x

values only
L
for the function
on the interval
@
0, 2
p
D
4. f
H
x
L
=
tan

1
H
2
x
L
Find the number
H
s
L
c that satisfies the Mean Value Theorem on the interval
A

è!!!!
3
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
2
,
3
ÄÄÄÄÄÄÄÄÄÄÄÄ
2
E
H
don
¢
t worry if the answer looksunsimplified, just make sure you solve for c
L
.
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View Full Document5. f
H
x
L
=
log
2
»
x
2

4
»
Find where the function is increasing and decreasing on its domain.
6. f
H
x
L
=
x
2
+
3
x
+
3I
f
x
1
=
1,
use Newton
¢
s Method to find x
2
and x
3
.
7. If
f
H
x
L
=
x
H
2
2
x
L
, then find where the graph of f
H
x
L
is concave up and concave down on the interval
H
•
,
•
L
.
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 Derivative, Convex function, HxL, DeRuiter, extreme values Hx

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