Which of the following conditions characterizes a critical point of as a…

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

Problem

Which of the following conditions characterizes a critical point of

y

as a differentiable function of

x

on an implicitly defined curve

F(x,y)=0

? (a)

\dfrac{dy}{dx}

is undefined only (b)

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

(c)

\dfrac{dy}{dx}=0 \text{ or } \dfrac{dy}{dx} \text{ is undefined}

(d)

\dfrac{dy}{dx}=0

only