Which of the following best describes the concavity of the curve at the point ?

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

Problem

Which of the following best describes the concavity of the curve x2+y2−4y=0x^{2}+y^{2}-4y=0 at the point (0,0)(0,0)? (a) Concave down, since d2ydx2<0\displaystyle \frac{d^{2}y}{dx^{2}}<0. (b) Indeterminate, because dydx\displaystyle \frac{dy}{dx} is undefined at (0,0)(0,0). (c) Concave up, since d2ydx2>0\displaystyle \frac{d^{2}y}{dx^{2}}>0. (d) An inflection point, since d2ydx2=0\displaystyle \frac{d^{2}y}{dx^{2}}=0.

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