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Mathematics
Problem
For the curve defined by
x
3
+
y
3
=
9
x
y
x^{3}+y^{3}=9xy
x
3
+
y
3
=
9
x
y
, which of the following lists all points on the curve where the tangent line is vertical? a)
(
0
,
0
)
(0,0)
(
0
,
0
)
b)
(
3
,
3
)
(3,3)
(
3
,
3
)
c)
(
54
2
/
3
3
,
54
1
/
3
)
\bigl(\dfrac{54^{\,2/3}}{3},\,54^{\,1/3}\bigr)
(
3
5
4
2/3
,
5
4
1/3
)
d)
(
54
1
/
3
,
54
2
/
3
3
)
\bigl(54^{\,1/3},\,\dfrac{54^{\,2/3}}{3}\bigr)
(
5
4
1/3
,
3
5
4
2/3
)
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