The point(s) on the curve y^3 + 3x^2 = 12y, where the tangent is vertical (i.e., parallel to the y-axis), is/are

JEE Advanced Mathematics question

The point(s) on the curve , where the tangent is vertical (i.e., parallel to the -axis), is/are

Answer: (D)

Differentiate implicitly: , so , i.e. . The tangent is vertical when : (with ), so .

- :

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Question ID VK-110607