A point is moving along the curve $y^{3} = 27 x$ . The interval in which the abscissa changes at slower rate than ordinate, is

(- 3, 3)

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(- \infty, \infty)

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(- 1, 1)

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(- \infty, - 3) \cup (3, \infty)

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Solution

The correct option is B $(- 1, 1)$
Assume $z = x - y = y^{3} / 27 - y$
given $\frac{d z}{d y} < 0 \Rightarrow y^{2} / 9 - 1 < 0$
$\Rightarrow y ϵ (- 3, 3) \Rightarrow x ϵ (- 1, 1)$

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