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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
−
2
f(x)=x-2
f
(
x
)
=
x
−
2
for
0
≤
x
≤
4
0\le x\le4
0
≤
x
≤
4
and define
F
(
x
)
=
∫
0
x
(
t
−
2
)
d
t
F(x)=\displaystyle\int_{0}^{x}(t-2)\,dt
F
(
x
)
=
∫
0
x
(
t
−
2
)
d
t
. Determine the interval(s) on
[
0
,
4
]
[0,4]
[
0
,
4
]
where
F
F
F
is (i) increasing, and (ii) decreasing.
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