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Mathematics
Mathematics
Problem
A continuous function
f
f
f
satisfies the sign pattern •
f
(
x
)
>
0
f(x)>0
f
(
x
)
>
0
on
(
−
4
,
−
2
)
(-4,-2)
(
−
4
,
−
2
)
and
(
1
,
5
)
(1,5)
(
1
,
5
)
•
f
(
x
)
=
0
f(x)=0
f
(
x
)
=
0
at
x
=
−
4
,
−
2
,
1
,
5
x=-4,-2,1,5
x
=
−
4
,
−
2
,
1
,
5
•
f
(
x
)
<
0
f(x)<0
f
(
x
)
<
0
on
(
−
2
,
1
)
(-2,1)
(
−
2
,
1
)
Let
F
(
x
)
=
∫
−
4
x
f
(
t
)
d
t
F(x)=\int_{-4}^{x} f(t)\,dt
F
(
x
)
=
∫
−
4
x
f
(
t
)
d
t
. Identify the open intervals where
F
F
F
is increasing and the open intervals where
F
F
F
is decreasing.
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