Question

On the curve $x^3=12y$, the abscissa changes at faster rate than the ordinate. Then $x$ belongs to the interval

• A. (-2, 2)
• B. (-1, 1)
• C. (0, 2)
• D. none of these

Answer 1

Answer: (A)

(-2, 2)

$x^3=12y$
Now
$3x^2.\frac{dx}{dt}=12.\frac{dy}{dt}$
Or
$x^2=4\frac{dy}{dx}$
Now
It is given
$dx>dy$
Or
$1>\frac{dy}{dx}$.
Hence
$\frac{x^2}{4}<1$
Or
$x^2<4$
Or
$-2<x<2$
Or
$xϵ(-2,2)$.