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Mathematics
Mathematics
Problem
Suppose
f
f
f
is continuous on
[
2
,
7
]
[2,7]
[
2
,
7
]
with
f
(
x
)
>
0
f(x)>0
f
(
x
)
>
0
for
2
<
x
<
5
2<x<5
2
<
x
<
5
and
f
(
x
)
<
0
f(x)<0
f
(
x
)
<
0
for
5
<
x
<
7
5<x<7
5
<
x
<
7
. The function
F
F
F
satisfies
F
′
(
x
)
=
f
(
x
)
F'(x)=f(x)
F
′
(
x
)
=
f
(
x
)
and
F
(
2
)
=
1
F(2)=1
F
(
2
)
=
1
. Indicate on which subintervals of
[
2
,
7
]
[2,7]
[
2
,
7
]
the function
F
F
F
is increasing and on which it is decreasing.
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