At a point on an implicitly defined curve where

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

Problem

\dfrac{dy}{dx}=0

, which of the following conditions on

\dfrac{d^{2}y}{dx^{2}}

most strongly indicates a local maximum of

y

with respect to

x

? (a)

\dfrac{d^{2}y}{dx^{2}}>0

(b)

\dfrac{d^{2}y}{dx^{2}}<0

(c)

\dfrac{d^{2}y}{dx^{2}}=0

(d) The sign of

\dfrac{d^{2}y}{dx^{2}}

is irrelevant