Question

A point moves along the curve $12y=x^3$ in such a way that the rate of increase of its ordinate is more than the rate of increase of abscissa. The abscissa of the point lies in the interval

• A. $(-2,2)$
• B. $(-\infty ,-2)U(2,\infty )$
• C. $[-2,2]$
• D. none of these

Answer 1

Answer: (B)

$(-\infty ,-2)U(2,\infty )$

$12y=x^3$

$\frac{dy}{dt}=\frac{x^2}{4}\frac{dx}{dt}$

Given , $\frac{dy}{dt}>\frac{dx}{dt}$

$\Rightarrow (x^2-4)\frac{dx}{dt}>0$

$\Rightarrow (x-2)(x+2)>0$

$\Rightarrow x\in (-\infty ,-2)U(2,\infty )$