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

7-46.

Consider the curve formed by the equation

*xy*^{2}−*x*^{3}*y*= 12. Homework Help ✎Show that

= . Find the

*x*-coordinate of each point on the curve where the tangent line is vertical.

Use implicit differentiation.

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.