For a parametric curve given by and

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

Problem

For a parametric curve given by

x=f(t)

and

y=g(t)

, which of the following conditions at

t=t_0

guarantees that the tangent to the curve is vertical? (a)

f'(t_0)=0 \text{ and } g'(t_0)=0

(b)

\displaystyle \left|\frac{g'(t_0)}{f'(t_0)}\right| \to \infty

(c)

f'(t_0)=0 \text{ and } g'(t_0)\ne 0

(d)

f'(t_0)\ne0 \text{ and } g'(t_0)=0