Mathematics

Problem

An implicitly defined curve yields the derivative

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

, where

N

and

D

are differentiable at a point

(x_0,y_0)

. Which of the following conditions is sufficient to guarantee that the curve has a horizontal tangent at

(x_0,y_0)

? a)

N(x_0,y_0)=0

and

D(x_0,y_0)=0

N(x_0,y_0)=0

and

D(x_0,y_0)\neq 0

D(x_0,y_0)=0

and

N(x_0,y_0)\neq 0

\dfrac{dy}{dx}

is undefined at

(x_0,y_0)