The graphs of
f
(
x
)
=
x
3
−
6
x
2
+
9
x
+
2
\displaystyle {f{{\left({x}\right)}}}={x}^{{3}}-{6}{x}^{{2}}+{9}{x}+{2}
f
(
x
)
=
x
3
−
6
x
2
+
9
x
+
2
and
g
(
x
)
=
3
x
2
−
15
x
+
18
\displaystyle {g{{\left({x}\right)}}}={3}{x}^{{2}}-{15}{x}+{18}
g
(
x
)
=
3
x
2
−
15
x
+
18
intersect at two points. At one of those intersections, the graphs are tangent to each other (meaning they have a common tangent line). Find the coordinates of that point.
x
=
\displaystyle {x}=
x
=
y
=
\displaystyle {y}=
y
=
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