First slide

Rate Measure

Question

$A point is moving along the cubical parabola 12 y = x^{3} . The rate of ordinate is less than the rate of abscissa when$

Moderate

A

$x < - 2 or x > 2$
B

$x = \pm 2$
C

$- 2 < x < 2$
D

$x = \pm 4$

Solution

$\begin{array}{l} 12 y = x^{3} \Rightarrow 12 \frac{d y}{d t} = 3 . x^{2} \cdot \frac{d x}{d t} \\ \Rightarrow 4 \cdot \frac{d y}{d t} = x^{2} \cdot \frac{d x}{d t} given \frac{d y}{d t} < \frac{d x}{d t} \\ \Rightarrow 4 > x^{2}, x^{2} < 4, x \in (- 2, 2) \end{array}$

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