For a differentiable parametric curve given by and

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

For a differentiable parametric curve given by

x=f(t)

and

y=g(t)

, which of the following conditions must hold at a point to guarantee that the tangent line is horizontal? (a)

\dfrac{dy}{dt}=0

(b)

\dfrac{dy}{dt}=0

and

\dfrac{dx}{dt}\neq 0

(c)

\dfrac{dx}{dt}=0

and

\dfrac{dy}{dt}\neq 0

(d)

\dfrac{dy}{dt}=0

and

\dfrac{dx}{dt}=0