Question

A particle is in motion along a curve $12y-x^3$. The rate of change of its ordinate exceeds that of abscissa in

• A. $-2<x<2$
• B. $x=\pm 2$
• C. $x<-2$
• D. $x>2$

Answer 1

Answer: (C), (D)

The correct options are
C $x>2$
D $x<-2$

Given $\frac{dy}{dt}>\frac{dx}{dt}....\left(1\right)$
and $12y-x^3$
$12\frac{dy}{dt}=3x^2\frac{dx}{dt}.....\left(ii\right)$
from (1) $3x^2\frac{dx}{dt}>12\frac{dx}{dt}\Rightarrow x^2-4>0\Rightarrow x\in (-\infty ,-2)\cup (2,\infty )$