In the study of parametric curves

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

Problem

In the study of parametric curves, the condition

f'(t)\neq0

is imposed mainly because it (a) to ensure that

\dfrac{dy}{dt}

exists (b) to guarantee that

x=f(t)

is monotonic throughout the interval (c) to prevent division by zero when forming

\dfrac{dy}{dx}

(d) to avoid sharp cusps by forcing the curvature to vanish