Practice Test IIIB for Math 1501, Calculus I
I
Let
a
and
b
be any two positive numbers such that
a
+
b
=4
.
(a)
How large can
ab
2
be? Find the values of
a
and
b
that make this as large as possible.
(b)
How large can
(
1
a
+
1
b
)

1
be? Find the values of
a
and
b
that make this as large as
possible.
II
Let
f
be the function
f
(
x
)=
p
x
2
+2
x

p
x
2
for
x>
0
.
(a)
Find all asymptotes of this function, if any.
(b)
Find all critical numbers for this function, if any.
(c)
For which values of
x
, if any, is this function increasing?
(d)
x
, if any, is this function decreasing?
(e)
Does the function have an absolute maximum?
III
Use the Mean Value Theorem to answer the following questions. Let
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This note was uploaded on 02/07/2011 for the course MATH 1501 taught by Professor N/a during the Fall '08 term at Georgia Tech.
 Fall '08
 N/A
 Calculus

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