A particle moves along the ellipse

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

9x^{2}+4y^{2}=36

. When the particle is in the first quadrant with

x=1\,\text{unit}

and

\dfrac{dx}{dt}=2\,\text{units s}^{-1}

, what is

\dfrac{dy}{dt}

? (a)

\sqrt{3}\,\text{units s}^{-1}

(b)

-\dfrac{2\sqrt{3}}{3}\,\text{units s}^{-1}

(c)

-\sqrt{3}\,\text{units s}^{-1}

(d)

-3\sqrt{3}\,\text{units s}^{-1}