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Q.

$On the curve y = x^{3}, the interval of values of x for which abscissa$ $changes at a faster rate than the ordinate.$

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a

$(\frac{- 1}{3}, \frac{1}{3})$

b

$[\frac{- 1}{3}, \frac{1}{3}]$

c

$(\frac{- 1}{\sqrt{3}}, \frac{1}{\sqrt{3}})$

d

$[\frac{- 1}{\sqrt{3}}, \frac{1}{\sqrt{3}}]$

answer is C.

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Detailed Solution

$Change in abscissa dx > change in ordinate dy$

$|\frac{d x}{d y}| > 1$

$\begin{array}{l} y = x^{3} \Rightarrow \frac{d y}{d x} = 3 x^{2} \\ |\frac{1}{3 x^{2}}| > 1 \Rightarrow |3 x^{2}| < 1 \\ - 1 < 3 x^{2} < 1 \Rightarrow \frac{- 1}{3} < x^{2} < \frac{1}{3} \\ x \in (\frac{- 1}{\sqrt{3}}, \frac{1}{\sqrt{3}}) \end{array}$

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