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MAC 2311
July 22, 2003
Exam II and KEY
Prof. S. Hudson
This was an
80 minute Exam.
1) [40 pts] Compute the derivative,
f
0
(
x
) (shortcuts are OK, but show all work);
a)
f
(
x
) = sin(
x
3
)
b)
f
(
x
) =
1
(2
x
+1)
3
c)
f
(
x
) =
√
x
+1
x
d)
f
(
x
) = ln(ln(
x
))
e)
f
(
x
) =
x
x
f)
f
(
x
) =
x
2
sin(
x
+ 1)
g)
f
(
x
) = csc(2
x
)
h)
f
(
x
) =
√
x
3
+ 1
2) [10 pts] A farmer has 200 yd of fence with which to construct 3 sides of a rectangular
pen. An existing long, straight wall will be the fourth side (you can ask about a picture).
What dimensions will maximize the area of the pen?
3) [10pts] A gas balloon is being ﬁlled at a rate of 100
π
cm
3
of gas per second. At what
rate is the radius of the balloon increasing when its radius is 10cm?
4) [10 pts] Find the maximum and minimum values of
f
(
x
) =
x
3

3
x
2

9
x
+5 on [

2
,
4].
5) [15 pts] Answer True or False. You do not have to explain.
The derivative of a product (
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 Calculus, Derivative

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