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Math 2253
Review Problems for Exam 3 (Chapter 4)
1.
Find the absolute maximum and minimum values of each function on the given
interval.
a)
,
1
)
(
2

=
x
x
f
2
1
≤
≤

x
b)
x
x
x
f
cos
4
2
)
(
+
=
,
]
,
0
[
π
2.
Find the extreme values of the function and where they occur.
a)
4
2
)
(
3
+

=
x
x
x
f
b)
1
)
(
2
+
=
x
x
x
f
3.
Find the value or values of c that satisfy the equation
)
(
)
(
)
(
c
f
a
b
a
f
b
f
′
=


in the
conclusion of the Mean Value Theorem for the following functions and intervals.
a)
]
1
,
0
[
,
2
3
)
(
2
+

=
x
x
x
f
b)
]
3
,
1
[
,
1
)
(

=
x
x
f
4.
Find all possible functions with the following derivative.
a)
x
y
2
=
′
b)
1
2

=
′
x
y
c)
1
2
3
2

+
=
′
x
x
y
d)
2
1
sin
2
x
x
x
y
+
+
=
′
5.
Use the Second Derivative Test to find any local extrema of the function
a)
)
1
(
2
)
(
2
2
x
x
x
f

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

=
6.
Find the length and width of a rectangle that has the perimeter 100 meters and the
maximum area.
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This homework help was uploaded on 01/23/2008 for the course MATH 2253 taught by Professor Pascu during the Fall '07 term at SPSU.
 Fall '07
 PASCU
 Math, Calculus

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