The points on the curve $y = x^{3},$ the tangents at which are inclined at an angle of $60^{0}$ to $x -$ axis are

Easy

A

$(3^{- \frac{1}{4}}, 3^{- \frac{3}{4}}), (- 3^{- \frac{1}{4}}, - 3^{- \frac{3}{4}})$
B

$(3^{- \frac{1}{2}}, 3^{- \frac{2}{5}}), (- 3^{- \frac{1}{3}}, - 3^{- \frac{2}{3}})$
C

$(2^{\frac{1}{4}}, 2^{- \frac{2}{5}}), (- 3^{- \frac{1}{2}}, - 3^{- \frac{1}{2}})$
D

$(3^{- \frac{1}{4}}, 3^{- \frac{3}{4}}), (- 3^{\frac{1}{3}}, - 3^{- \frac{2}{3}})$

Solution

$\frac{d y}{d x} = 3 x^{2} \Rightarrow \sqrt{3} = 3 x^{2} \Rightarrow x = \pm 3^{- \frac{1}{4}}, y = \pm 3^{- \frac{3}{4}}$
$∴$ point $= (3^{- \frac{1}{4}}, 3^{- \frac{3}{4}}), (- 3^{- \frac{1}{4}}, - 3^{- \frac{3}{4}})$

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