Homework Help: 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