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Mathematics
Problem
Consider the function
f
(
x
)
=
x
2
+
3
x
+
2
f(x)=x^{2}+3x+2
f
(
x
)
=
x
2
+
3
x
+
2
on the interval
[
1
,
4
]
[1,4]
[
1
,
4
]
. (i) Calculate the average value
f
ˉ
\bar f
f
ˉ
of
f
f
f
on
[
1
,
4
]
[1,4]
[
1
,
4
]
. (ii) Find all real numbers
c
c
c
in
(
1
,
4
)
(1,4)
(
1
,
4
)
that satisfy
f
(
c
)
=
f
ˉ
f(c)=\bar f
f
(
c
)
=
f
ˉ
. Show each step of your working.
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