9.
[
2
4.7, 4.7] by [
2
3.1, 3.1]
(a)
f
9
(
x
)
5
x
?
}
2
ˇ
4
w
1
2
w
x
w
}
(
2
1)
1
ˇ
4
w
2
w
x
w
5
}
2
2
ˇ
3
x
4
w
1
2
w
8
x
w
}
The local extrema occur at the critical point
x
5 }
8
3
}
and
at the endpoint
x
5
4. There is a local (and absolute)
maximum at
1
}
8
3
}
,
}
3
ˇ
16
3
w
}
2
or approximately (2.67, 3.08),
and a local minimum at (4, 0).
(b)
Since
f
9
(
x
)
.
0 on
1
2‘
,
}
8
3
}
2
,
f
(
x
) is increasing on
1
2‘
,
}
8
3
}
4
.
(c)
Since
f
9
(
x
)
,
0 on
1
}
8
3
}
,4
2
,
f
(
x
) is decreasing on
3
}
8
3
}
4
.
10.
[
2
5, 5] by [
2
15, 15]
(a)
g
9
(
x
)
5
x
1/3
(1)
1 }
1
3
}
x
2
2/3
(
x
1
8)
5 }
4
3
x
x
1
2/3
8
}
The local extrema can occur at the critical points
x
52
2 and
x
5
0, but the graph shows that no extrema
occurs at
x
5
0. There is a local (and absolute)
minimum at (
2
2,
2
6
ˇ
3
2
w
) or approximately
(
2
2,
2
7.56).
(b)
Since
g
9
(
x
)
.
0 on the intervals (
2
2, 0) and (0,
‘
), and
g
(
x
) is continuous at
x
5
0,
g
(
x
) is increasing on
[
2
2,
‘
).
(c)
Since
g
9
(
x
)
,
0 on the interval (
2‘
,
2
2),
g
(
x
) is
decreasing on (
2‘
,
2
2].
11.
[
2
5, 5] by [
2
0.4, 0.4]
(a)
h
9
(
x
)
55
}
(
x
x
2
2
1
2
4
4
)
2
}
5
}
(
x
1
(
x
2
2
1
)(
x
4
2
)
2
2)
}
The local extrema occur at the critical points,
x
56
2.
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 Fall '08
 GERMAN

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