Suppose the derivative of an implicit curve can be written as

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

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

. Explain in a sentence why the curve has a horizontal tangent at points where

N(x,y)=0

but

D(x,y)\neq 0