### Home > CALC > Chapter 7 > Lesson 7.1.4 > Problem7-46

7-46.

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

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

Use implicit differentiation.

2. Find 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.