The curve is defined by and

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

Problem

The curve is defined by

x(t)=t^{3}-3t

and

y(t)=t^{2}

. Which statement correctly characterizes the tangent line to the curve at

t=1

? (a) The tangent line has slope

2

, obtained from

\dfrac{dy}{dt}

evaluated at

t=1

. (b) The tangent line is horizontal because

\dfrac{dy}{dx}=0

t=1

. (c) The tangent line is vertical because

\dfrac{dy}{dx}

is undefined (division by zero) at

t=1

. (d) The tangent line has slope

\dfrac{1}{3}

, found by computing

\dfrac{dy/dt}{3t^{2}+3}

t=1