On the curve

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

Problem

On the curve x2=y3−3yx^{2}=y^{3}-3y, identify all critical points. For any critical point where d2ydx2=0\dfrac{d^{2}y}{dx^{2}}=0, explain briefly why the second–derivative test is inconclusive there and state whether the point is a local extremum or a saddle point.

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