Consider the curve

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Consider the curve x2−xy+y2=3x^{2}-xy+y^{2}=3. With respect to xx, the curve at the point (1,1)(1,1) is (a) concave up because d2ydx2>0\dfrac{d^{2}y}{dx^{2}}>0 there (b) concave down because dydx<0\dfrac{dy}{dx}<0 there (c) concave down because d2ydx2<0\dfrac{d^{2}y}{dx^{2}}<0 there (d) a point of inflection because d2ydx2=0\dfrac{d^{2}y}{dx^{2}}=0 there

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