The curve is an astroid

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

Problem

The curve

x^{2/3}+y^{2/3}=4^{2/3}

is an astroid. Determine all points on the curve where

\dfrac{dy}{dx}

is undefined.

Related theory

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

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