30.
f
(
x
)
5
e
x
1
sin
x
f
9
(
x
)
5
e
x
1
cos
x
L
(
x
)
5
f
(0)
1
f
9
(0)(
x
2
0)
5
1
1
2(
x
2
0)
5
2
x
1
1
31.
The global minimum value of
}
1
2
}
occurs at
x
5
2.
32. (a)
The values of
y
9
and
y
0
are both negative where the
graph is decreasing and concave down, at
T
.
(b)
The value of
y
9
is negative and the value of
y
0
is posi
tive where the graph is decreasing and concave up, at
P
.
33. (a)
The function is increasing on the interval (0, 2].
(b)
The function is decreasing on the interval [
2
3, 0).
(c)
The local extreme values occur only at the endpoints of
the domain. A local maximum value of 1 occurs at
x
5 2
3, and a local maximum value of 3 occurs at
x
5
2.
34.
The 24th day
35.
36. (a)
We know that
f
is decreasing on [0, 1] and increasing
on [1, 3], the absolute minimum value occurs at
x
5
1
and the absolute maximum value occurs at an endpoint.
Since
f
(0)
5
0,
f
(1)
5 2
2, and
f
(3)
5
3, the absolute
minimum value is
2
2 at
x
5
1 and the absolute maxi
mum value is 3 at
x
5
3.
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 Spring '08
 GERMAN
 Derivative, Mathematical analysis, Convex function

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