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Mathematics
Mathematics
Problem
Let
g
(
x
)
=
∫
3
x
f
(
t
)
d
t
g(x)=\displaystyle\int_{3}^{x} f(t)\,dt
g
(
x
)
=
∫
3
x
f
(
t
)
d
t
, where
f
f
f
is continuous and
f
(
t
)
>
0
f(t)>0
f
(
t
)
>
0
for every
t
t
t
in the interval
(
1
,
4
)
(1,4)
(
1
,
4
)
. Describe the monotonic behavior of
g
g
g
on
(
1
,
4
)
(1,4)
(
1
,
4
)
.
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