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Mathematics
Problem
Let
f
(
x
)
=
x
3
−
6
x
2
+
9
x
+
2
f(x)=x^{3}-6x^{2}+9x+2
f
(
x
)
=
x
3
−
6
x
2
+
9
x
+
2
be defined on
[
0
,
4
]
[0,4]
[
0
,
4
]
. Determine all points
c
∈
(
0
,
4
)
c\in(0,4)
c
∈
(
0
,
4
)
at which
f
′
(
c
)
f'(c)
f
′
(
c
)
equals the average rate of change of
f
f
f
over
[
0
,
4
]
[0,4]
[
0
,
4
]
.
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