Which one of the following conditions guarantees a horizontal tangent to the…

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

Problem

Which one of the following conditions guarantees a horizontal tangent to the parametric curve

x=f(t),\;y=g(t)

t=t_{0}

? (a)

f'(t_{0})=0

and

g'(t_{0})\neq0

(b)

g'(t_{0})=0

and

f'(t_{0})=0

(c)

g'(t_{0})=0

and

f'(t_{0})\neq0

(d)

f'(t_{0})=g'(t_{0})\neq0