Describe how the values of and at a critical point of an implicitly defined curve…

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Describe how the values of

\dfrac{dy}{dx}

and

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

at a critical point of an implicitly defined curve determine whether that point is a local maximum, a local minimum, or neither.