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Mathematics
Problem
The point(s) on the curve
y
3
+
3
x
2
=
12
y
y^3 + 3x^2 = 12y
y
3
+
3
x
2
=
12
y
, where the tangent is vertical, is (are) (a)
(
±
4
3
,
−
2
)
\left(\pm \frac{4}{\sqrt{3}}, -2\right)
(
±
3
4
,
−
2
)
(b)
(
±
11
3
,
1
)
\left(\pm \sqrt{\frac{11}{3}}, 1\right)
(
±
3
11
,
1
)
(c)
(
0
,
0
)
(0, 0)
(
0
,
0
)
(d)
(
±
4
3
,
2
)
\left(\pm \frac{4}{\sqrt{3}}, 2\right)
(
±
3
4
,
2
)
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