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Mathematics
Mathematics
Problem
The function
f
(
x
)
=
x
e
x
(
1
−
x
)
f(x) = xe^{x(1-x)}
f
(
x
)
=
x
e
x
(
1
−
x
)
,
x
∈
R
x \in \mathbb{R}
x
∈
R
, is (A) increasing in
(
−
1
2
,
1
)
\left(-\frac{1}{2}, 1\right)
(
−
2
1
,
1
)
(B) decreasing in
(
1
2
,
2
)
\left(\frac{1}{2}, 2\right)
(
2
1
,
2
)
(C) increasing in
(
−
1
,
−
1
2
)
\left(-1, -\frac{1}{2}\right)
(
−
1
,
−
2
1
)
(D) decreasing in
(
−
1
2
,
1
2
)
\left(-\frac{1}{2}, \frac{1}{2}\right)
(
−
2
1
,
2
1
)
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