Implicit Differentiation - Vertical and Horizontal Tangents
Finding the vertical and horizontal tangent lines to an implicitly defined curve. We find the first derivative and then consider the cases:
Horizontal tangent line means slope is zero, slope is zero means derivative is zero. Find the relationship between x and y that makes that happen, substitute into original equation to solve for x and y.
Vertical tangent means slope is undefined; slope undefined means derivative is undefined, which means the denominator of the derivative is zero.