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Mathematics
Problem
Let
f
(
x
)
=
x
3
−
6
x
2
+
9
x
f(x)=x^{3}-6x^{2}+9x
f
(
x
)
=
x
3
−
6
x
2
+
9
x
for
0
≤
x
≤
4
0\le x\le 4
0
≤
x
≤
4
and define
g
(
x
)
=
∫
0
x
f
(
t
)
d
t
g(x)=\displaystyle\int_{0}^{x} f(t)\,dt
g
(
x
)
=
∫
0
x
f
(
t
)
d
t
. Determine all values of
x
x
x
in
(
0
,
4
)
(0,4)
(
0
,
4
)
at which
g
g
g
has a point of inflection, and justify your answer in one or two sentences.
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