Question

On the curve $x^3=12y$ , then the interval at which the abscissa changes at a faster rate than the ordinate ?

• A. $x\in (-2,2)$
• B. $x\in (-2,2)-\left\{0\right\}$
• C. $x\in (-3,3)-\left\{0\right\}$
• D. None of these

Answer 1

Answer: (A)

$x\in (-2,2)$

$\left|dy\right|>\left|dx\right|$

$\left|\frac{dy}{dx}\right|>1$

$x^3=12y$

diff wrto y

$3x^2\frac{dx}{dy}=12$

$\frac{dx}{dy}=\frac{12}{{3x}^2}=\frac{4}{x^2}$

$\left|\frac{dy}{dx}\right|>1$

$\left|\frac{y}{x^2}\right|>1$

$\left|x^2\right|>4$

$x>\pm 2$

$(2,-2)$