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Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
x
e
−
x
f(x)=x e^{-x}
f
(
x
)
=
x
e
−
x
defined for
x
>
0
x>0
x
>
0
. For which of the following intervals is
f
f
f
both increasing and concave down? a)
(
1
,
2
)
(1,2)
(
1
,
2
)
b)
(
0
,
1
)
(0,1)
(
0
,
1
)
c)
(
0
,
2
)
(0,2)
(
0
,
2
)
d)
(
2
,
∞
)
(2,\infty)
(
2
,
∞
)
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