Consider the curve formed by the equation $xy^2 − x^3y = 12$.

1. Show that $\frac { d y } { d x }=\frac { 3 x ^ { 2 } y - y ^ { 2 } } { 2 x y - x ^ { 3 } }$.

   Hint (a):

   Use implicit differentiation.

2. Find the $x$-coordinate of each point on the curve where the tangent line is vertical.

   Hint 1(b):

   A tangent line will be vertical where the denominator of the derivative = 0.

   Hint 2(b):

   Since the denominator has both x and y values, there will be infinitely many ways to make the denominator equal to 0.
   But only some (or one) of those ways fit the given curve.