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Mathematics
Mathematics
Problem
A function
f
f
f
is continuous on
[
0
,
8
]
[0,8]
[
0
,
8
]
with
g
(
x
)
=
∫
0
x
f
(
t
)
d
t
g(x)=\int_{0}^{x} f(t)\,dt
g
(
x
)
=
∫
0
x
f
(
t
)
d
t
. Suppose
g
(
8
)
=
20
g(8)=20
g
(
8
)
=
20
and
f
(
4
)
=
3
f(4)=3
f
(
4
)
=
3
. Decide whether the average value of
f
f
f
on
[
0
,
8
]
[0,8]
[
0
,
8
]
is greater than, equal to, or less than
f
(
4
)
f(4)
f
(
4
)
, and support your conclusion with a numerical argument.
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