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Mathematics
Mathematics
Problem
Let
F
(
x
)
=
∫
2
x
f
(
t
)
d
t
F(x)=\displaystyle\int_{2}^{x} f(t)\,dt
F
(
x
)
=
∫
2
x
f
(
t
)
d
t
, where
f
f
f
is continuous. Suppose
f
(
t
)
>
0
f(t)>0
f
(
t
)
>
0
for
3
<
t
<
6
3<t<6
3
<
t
<
6
and
f
(
t
)
<
0
f(t)<0
f
(
t
)
<
0
for
6
<
t
<
8
6<t<8
6
<
t
<
8
. Determine the open intervals within
(
3
,
8
)
(3,8)
(
3
,
8
)
on which
F
F
F
is increasing and the intervals on which
F
F
F
is decreasing.
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