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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
2
f(x)=x^{2}
f
(
x
)
=
x
2
on the interval
[
0
,
2
]
[0,2]
[
0
,
2
]
. Determine a value of
c
c
c
in
[
0
,
2
]
[0,2]
[
0
,
2
]
for which
f
(
c
)
f(c)
f
(
c
)
equals the average value of
f
f
f
on that interval. Express
c
c
c
exactly.
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