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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
2
+
3
f(x)=x^{2}+3
f
(
x
)
=
x
2
+
3
on the interval
[
1
,
4
]
[1,4]
[
1
,
4
]
. (i) Calculate the average value of
f
f
f
on
[
1
,
4
]
[1,4]
[
1
,
4
]
. (ii) Determine all numbers
c
c
c
in
(
1
,
4
)
(1,4)
(
1
,
4
)
for which
f
(
c
)
f(c)
f
(
c
)
equals the average value found in part (i).
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