For an implicitly defined curve

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

For an implicitly defined curve, the derivative can often be written in the form dydx=N(x,y)D(x,y)\dfrac{dy}{dx}=\dfrac{N(x,y)}{D(x,y)}, where NN and DD 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 and D(x,y)≠0N(x,y)=0 \text{ and } D(x,y)\neq 0 (b) D(x,y)=0 and N(x,y)≠0D(x,y)=0 \text{ and } N(x,y)\neq 0 (c) N(x,y)=0 and D(x,y)=0N(x,y)=0 \text{ and } D(x,y)=0 (d) D(x,y)=0 (with no restriction on N(x,y))D(x,y)=0\text{ (with no restriction on }N(x,y))

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