Implicit differentitaion and finding coordinates

[brambleberry]

Homework Statement

dy/dx = [3(x^2)y - y^2] / [2xy - x^3]

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

Homework Equations

original equation is x(y^2) - (x^3)y = 6

The Attempt at a Solution

i set the denominator of the deriv. to 0, but i have no idea where to go from there. am i solving for x or y? is there a way i can eliminate one of the variables? do i need to plug anything into the orig. equation?

 

[snipez90]

You have two equations and two variables so it shouldn't be difficult to get what you need. Setting the denominator to zero, you can solve for y. Then using the original equation, you can solve for x.

 

[brambleberry]

You have two equations and two variables so it shouldn't be difficult to get what you need. Setting the denominator to zero, you can solve for y. Then using the original equation, you can solve for x.

i don't know how to solve for y using the equation x(y^2) - (x^3)y = 6...i get stuck

 

[jgens]

Try this: the denominator equals x(2y - x^2), therefore, using the zero product property, the denominator is equal to zero when x = 0 and 2y = x^2. Use the second equation with the original to determine which values of x and y work.