A point moves along a curve given by

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

Problem

4x^{2}+y^{2}=25+2t

, where

t

is measured in seconds. At time

t=3\text{ s}

the point has coordinates

(2,\sqrt{15})

and

\dfrac{dx}{dt}=-0.5\text{ units/s}

. What is

\dfrac{dy}{dt}

at that moment? (a)

-\dfrac{\sqrt{15}}{3}\text{ units/s}

(b)

\dfrac{2\sqrt{15}}{3}\text{ units/s}

(c)

\dfrac{\sqrt{15}}{3}\text{ units/s}

(d)

\dfrac{4\sqrt{15}}{15}\text{ units/s}