On the curve x3=12y, the values of x for which the abscissa changes at a faster rate than the ordinate is - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

$3 x^{2} \frac{d x}{d y} = 12 \Rightarrow \frac{d x}{d y} = \frac{4}{x^{2}}$ . We need $|\frac{d x}{d y}| > 1$

$\Rightarrow \frac{4}{x^{2}} > 1 \Rightarrow x^{2} < 4, x \neq 0 \Rightarrow x \in (- 2, 2) ~ {0}$

On the curve $x^{3} = 12 y$ , the values of $x$ for which the abscissa changes at a faster rate than the ordinate is