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Mathematics
Mathematics
Problem
A differentiable function
f
f
f
satisfies
f
′
(
x
)
<
0
(
0
<
x
<
2
)
,
f
′
(
x
)
>
0
(
2
<
x
<
4
)
,
f
′
(
x
)
<
0
(
4
<
x
<
6
)
.
f'(x)<0\quad (0<x<2),\qquad f'(x)>0\quad (2<x<4),\qquad f'(x)<0\quad (4<x<6).
f
′
(
x
)
<
0
(
0
<
x
<
2
)
,
f
′
(
x
)
>
0
(
2
<
x
<
4
)
,
f
′
(
x
)
<
0
(
4
<
x
<
6
)
.
Let
F
(
x
)
=
∫
0
x
f
(
t
)
d
t
F(x)=\int_{0}^{x} f(t)\,dt
F
(
x
)
=
∫
0
x
f
(
t
)
d
t
. Determine all
x
x
x
in
(
0
,
6
)
(0,6)
(
0
,
6
)
at which
F
F
F
has an inflection point.
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