The point lies on the upper half of the circle defined implicitly by

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

Problem

The point (0,1)(0,1) lies on the upper half of the circle defined implicitly by x2+y2=1x^{2}+y^{2}=1. When yy is expressed as a function of xx near this point, what is y′′′(0)y'''(0)? (a) 11 (b) −1-1 (c) 00 (d) 22

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