The equation of a curve is

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

Problem

The equation of a curve is x2+y2=5x^{2}+y^{2}=5. Implicit differentiation shows that dydx\dfrac{dy}{dx} would be undefined at the point (3,0)(3,0). Explain, in one or two sentences, why (3,0)(3,0) is nevertheless not a critical point of the curve.

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