Mathematics

Problem

For an implicitly defined curve, the derivative can often be written in the form

\dfrac{dy}{dx}=\dfrac{N(x,y)}{D(x,y)}

, where

N

and

D

are differentiable functions. Which condition must be satisfied at a point on the curve for the tangent line there to be vertical? a)

N(x,y)=0 \text{ and } D(x,y)\neq 0

D(x,y)=0 \text{ and } N(x,y)\neq 0

N(x,y)=0 \text{ and } D(x,y)=0

D(x,y)=0\text{ (with no restriction on }N(x,y))