For the curve defined implicitly by

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

Problem

For the curve defined implicitly by x2+xy+y2=9x^{2}+xy+y^{2}=9, at which xx–value(s) does yy attain a relative extremum with respect to xx on branches where dydx\dfrac{dy}{dx} is defined? (a) x=3x=\sqrt{3} \text{ only} (b) x=±3x=\pm\sqrt{3} (c) x=±23x=\pm2\sqrt{3} (d) \text{No real }x\text{–values}

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