A particle moves so that its position at time is given by and

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

A particle moves so that its position at time

t

is given by

x(t)=t^{2}+1

and

y(t)=\dfrac{1}{t}

, where

t>0

. Determine the slope

\dfrac{dy}{dx}

of the particle’s path at

t=2

. (a)

-\dfrac{1}{4}

(b)

\dfrac{1}{16}

(c)

-\dfrac{1}{16}

(d)

-\dfrac{1}{8}