At a point P on the curve given implicitly by F(x,y)=0

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

Problem

At a point P on the curve given implicitly by F(x,y)=0, it is known that

\dfrac{dy}{dx}=0

and

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

. Which of the following best describes the behavior of the curve at P? (a)

P

is a saddle point (a point of inflection) on the curve. (b)

P

is a local maximum of

y

with respect to

x

. (correct) (c) The information given is insufficient to classify

P

. (d)

P

is a local minimum of

y

with respect to

x