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Mathematics
Mathematics
Problem
A continuous function
f
f
f
satisfies
f
(
t
)
>
0
f(t)>0
f
(
t
)
>
0
for
0
<
t
<
3
0<t<3
0
<
t
<
3
and
f
(
t
)
<
0
f(t)<0
f
(
t
)
<
0
for
3
<
t
<
6
3<t<6
3
<
t
<
6
. Let
G
(
x
)
=
∫
0
x
f
(
t
)
d
t
G(x)=\int_{0}^{x} f(t)\,dt
G
(
x
)
=
∫
0
x
f
(
t
)
d
t
. Describe whether
G
G
G
is increasing or decreasing on the intervals
(
0
,
3
)
(0,3)
(
0
,
3
)
and
(
3
,
6
)
(3,6)
(
3
,
6
)
.
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