MA 121
TEST
2
Please show all of your work in answering the following:
1.
Let
f x
x
x
x
( )
=
−
−
−
2
9
60
6
3
2
a)
Find the intervals on which
f
is increasing or decreasing.
b)
Identify all relative extrema.
c)
Find the intervals on which
f
is concave up or concave down.
d)
Sketch the curve.
2.
Find the absolute maximum and the absolute minimum of
f x
x
x
( )
=
+
2
4
on the interval [ 1, 1 ].
3.
Sketch the graph of
f x
x
x
( )
=
+
2
1
, identifying relative extrema, inflection points,
asymptotes, etc.
4.
Find
′
y
when
a)
y
x e
x
=
−
1
2
b)
y
e
x
x
=
−
+
3
5
2
2
c)
y
e
x
=
+
(
)
2
5
1
d)
y
x
=
5
3
ln
e)
y
x
x
=
+
+
ln
2
1
2
f)
y
x
=
8
3
g)
y
x
x
=
4
4
h)
y
x
x
x
=
−
−
ln(
)
3
2
1
4
3
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5.
The half life of lead is 22 years.
a)
Find its decay rate.
b)
If you initially have 15 grams of lead, how long until only 10 grams remain?
6.
An open box is to be constructed from a piece of cardboard
that is 18 in. by 18 in. by
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