Mathematics

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

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

\dfrac{dy}{dx}=0

only