# Need help factoring in two variables

1. Sep 17, 2011

### Dannbr

1. The problem statement, all variables and given/known data

Trying to find relative min/max

2. Relevant equations

f(x,y)=X^4+y^4-36xy

3. The attempt at a solution

partial WRT(x) = 4x^3-36y
partial WRT(y) = 4y^3-36x

Set Partial WRT(x) = 0

4x^3-36y=0
4x^3=36y
x=(9y)^1/3

plug x into Partial

4[(9y)^1/3]^3-36y=0
36y-36y=0

Im not sure what to do now to find the critical points?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 17, 2011

### Harrisonized

Let ∂f/∂x=0 and ∂f/∂y=0.

From your original post, you have

∂f/∂x = 4x3-36y = 4(x3-9y) = 0
∂f/∂y = 4y3-36x = 4(y3-9x) = 0

Now all you have left to do is to find all points that satisfy both equations. Two equations. Two unknowns. Algebra holds the answer.

Last edited: Sep 17, 2011
3. Sep 17, 2011

### Dick

You just plugged your solution for WRT(x) back into the equation WRT(x). You aren't going to get anything out of that. Try solving the WRT(x) equation for y and putting that into the WRT(y) equation. You'll get an equation of high degree, but it's pretty easy to say what the possible real roots are.

4. Sep 17, 2011

### Dannbr

Thanks for help