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Mathematics
Problem
Let
f
f
f
be a twice-differentiable function with
f
′
(
x
)
=
(
x
−
3
)
e
−
x
,
f
′
′
(
x
)
=
(
−
x
+
2
)
e
−
x
.
f'(x)=(x-3)e^{-x},\qquad f''(x)=(-x+2)e^{-x}.
f
′
(
x
)
=
(
x
−
3
)
e
−
x
,
f
′′
(
x
)
=
(
−
x
+
2
)
e
−
x
.
Determine the set of all real numbers
x
x
x
for which
f
f
f
is decreasing and concave up simultaneously.
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