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44. continued
Note that
2}
1
2
}
x
2 }
1
2
}
5
0 when
x
52
1, and
3
x
2
2
12
x
1
8
5
0 when
x
5
5
}
12
6
6
ˇ
4
w
8
w
}5
2
6 }
2
ˇ
3
3
w
}
.
But 2
2 }
2
ˇ
3
3
w
}
<
0.845
,
1, so the only critical points
occur at
x
52
1 and
x
5
2
1 }
2
ˇ
3
3
w
}
<
3.155.
45.
Graph (c), since this is the only graph that has positive
slope at
c
.
46.
Graph (b), since this is the only graph that represents a
differentiable function at
a
and
b
and has negative slope
at
c
.
47.
Graph (d), since this is the only graph representing a
function that is differentiable at
b
but not at
a
.
48.
Graph (a), since this is the only graph that represents a
function that is not differentiable at
a
or
b
.
49. (a)
V
(
x
)
5
160
x
2
52
x
2
1
4
x
3
V
9
(
x
)
5
160
2
104
x
1
12
x
2
5
4(
x
2
2)(3
x
2
20)
The only critical point in the interval (0, 5) is at
x
5
2.
The maximum value of
V
(
x
) is 144 at
x
5
2.
(b)
The largest possible volume of the box is 144 cubic
units, and it occurs when
x
5
2.
50. (a)
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 Fall '08
 GERMAN
 Critical Point

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