Question

A particle is in motion along a curve \(12 y=x^{3}\). 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

Ans : (C, D)
Hint : \(12 \frac{d y}{d t}=3 x^{2} \frac{d x}{d t}\)
$$
\frac{\frac{d y}{d t}}{\frac{d x}{d t}} \geq 1 \quad \Rightarrow \frac{3 x^{2}}{12} \geq 1, \quad \Rightarrow x^{2} \geq 4, \quad \Rightarrow x \in(-\infty,-2] \cup[2, \infty)
$$

Answer 2

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