### Home > APCALC > Chapter 7 > Lesson 7.1.4 > Problem7-43

7-43.

Consider the equation $xy^2 - x^3y = 12$.

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

Use implicit differentiation.

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

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

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.