NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

The number of point(s) on the curve y 3 = 12 y - 3 x 2 where a tangent is vertical is/are

Correct answer

Step-by-step solution

y 3 = 12 y - 3 x 2 3 y 2 d y d x = 12 d y d x - 6 x d y d x = 2 x 4 - y 2 Tangent is vertical so 4 - y 2 = 0 ⇒ y = ± 2 At y = 2 ⇒ 8 = 24 - 3 x 2 x = ± 4 3 At y = - 2 ⇒ - 8 = - 24 - 3 x 2 x 2 is negative so x ∉ R So, the required points are 4 3 , 2   &   - 4 3 , 2 Hence, the number of points is 2

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