For an implicitly defined curve

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

Problem

For an implicitly defined curve F(x,y)=0F(x,y)=0, suppose the derivative obtained by implicit differentiation can be written in the form N(x,y)D(x,y)\dfrac{N(x,y)}{D(x,y)}. State the simultaneous conditions on NN and DD that must hold at a point (a,b)(a,b) for the tangent line to the curve to be horizontal at that point.

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