For the curve defined by

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

Problem

For the curve defined by y3+xy2−x2=1y^{3}+xy^{2}-x^{2}=1, find all points on the curve where dydx=0\dfrac{dy}{dx}=0 and classify each as a local maximum, a local minimum, or a saddle point.

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