# How do I find the possible y values in the following equation?

1. Apr 20, 2013

### Pizzerer

How do I find the potential y values for 32y^3-168y+100=0

It's a multi-variable calc problem. I have to find the critical points of the surface
f(x,y) = 10yx^2 - 5x^2 - 4y^2-x^4-2y^4

∂f/∂x = 20xy-10x-4x^3 = 0
x=0 or x^2 = (20y-10)/4

∂f/∂y = 8y^3+8y-10x^2=0

I subbed x^2 in and got 32y^3-168y+100=0

Any ideas what I'm doing wrong if I am? Or do I have to find the y values that satisfy 32y^3-168y+100=0?

Thanks for reading, guys.

Edit: Just realized I should've posted this in the homework help section. Don't know how to delete. Mod could you move this for me?

Last edited: Apr 20, 2013
2. Apr 20, 2013

### Staff: Mentor

You can report your own post to get it moved.

While there are formulas for those equations, I doubt that you have to use them. A numerical solution could be fine. The case x=0 is easier to study.

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