What are the extrema of f(x)=e−x2 on [−.5,a], where a>1?
Answers
Answered by
0
Answer:
f
(
16
)
=
e
256
8
and
f
(
0
)
=
0
Explanation:
f
'
=
(
1
128
)
(
x
e
x
2
)
'
=
(
1
128
)
(
(
x
)
'
e
x
2
+
(
e
x
2
)
'
x
)
=
(
1
128
)
e
x
2
(
1
+
2
x
2
)
Here,
e
x
2
≥
1
and
1
+
2
x
2
≥
1
. So, f'>=1>0#
And so, f is an increasing function in
x
∈
(
−
∞
,
∞
)
As
|
f
(
−
5
)
|
=
(
5
128
)
e
25
<
f
(
16
)
=
e
256
8
,
the absolute maximum =
f
(
16
)
=
e
256
8
and,
as
|
f
|
≥
0
and
f
(
0
)
=
0
,
the absolute minimum=
f
(
0
)
=
0
.
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