Explain why a parametric curve has a vertical tangent at a value when while .

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

Problem

Explain why a parametric curve

\bigl(x(t),\,y(t)\bigr)

has a vertical tangent at a value

t=a

when

\left.\dfrac{dx}{dt}\right|_{t=a}=0

while

\left.\dfrac{dy}{dt}\right|_{t=a}\neq 0