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Mathematics
Problem
Let
f
(
x
)
=
x
2
+
2
x
+
1
f(x)=x^{2}+2x+1
f
(
x
)
=
x
2
+
2
x
+
1
for
−
1
≤
x
≤
3
-1\le x\le 3
−
1
≤
x
≤
3
. (a) Calculate the average value of
f
f
f
on the interval
[
−
1
,
3
]
[-1,3]
[
−
1
,
3
]
. (b) Determine all value(s) of
c
c
c
in
[
−
1
,
3
]
[-1,3]
[
−
1
,
3
]
for which
f
(
c
)
f(c)
f
(
c
)
equals the average value found in part (a). Show algebraic work leading to each solution.
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