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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
3
−
6
x
2
+
9
x
f(x)=x^{3}-6x^{2}+9x
f
(
x
)
=
x
3
−
6
x
2
+
9
x
for all real
x
x
x
, and define
F
(
x
)
=
∫
0
x
f
(
t
)
d
t
F(x)=\displaystyle \int_{0}^{x} f(t)\,dt
F
(
x
)
=
∫
0
x
f
(
t
)
d
t
. On which of the following intervals is
F
F
F
concave up? a)
(
1
,
∞
)
(1,\infty)
(
1
,
∞
)
b)
(
−
∞
,
1
)
(-\infty,1)
(
−
∞
,
1
)
c)
(
−
∞
,
1
)
∪
(
3
,
∞
)
(-\infty,1)\cup(3,\infty)
(
−
∞
,
1
)
∪
(
3
,
∞
)
d)
(
1
,
3
)
(1,3)
(
1
,
3
)
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