The folium defined by possesses exactly one regular point where its tangent line is…

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

Problem

The folium defined by

x^{3}+y^{3}-3xy=0

possesses exactly one regular point where its tangent line is horizontal. Find the exact coordinates of this point.

Related theory

Implicit Curves
Advanced Differentiation
Implicit and parametric differentiation
Derivatives of implicit functions
Continuity and Differentiability

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