Consider a smooth parametric curve given by and

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

Problem

Consider a smooth parametric curve given by

x=f(t)

and

y=g(t)

. At

t=a

the derivatives satisfy

\dfrac{dx}{dt}=0

and

\dfrac{dy}{dt}\neq 0

. Which statement best describes the tangent line to the curve at the point corresponding to

t=a

? (a) The tangent line is horizontal because

\dfrac{dy}{dx}=0

. (b) The slope of the tangent line equals

\dfrac{dy}{dt}

evaluated at

t=a

. (c) The tangent line is vertical because

\dfrac{dy}{dx}

is undefined. (d) No tangent line exists because

\dfrac{dx}{dt}=0