# Homework Help: Optimization using Lagrange multipliers

1. Mar 22, 2009

### tinkus

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

f$$\left(x,y\right)$$ = x^2 +y^2
g$$\left(x,y\right)$$ = x^4+y^4 = 2
Find the maximum and minimum using Lagrange multiplier

2. Relevant equations

3. The attempt at a solution

2x=4x^3λ and 2y= 4y^3λ
2x^2 = 2y^2
x^2=y^2
x= $$\pm$$y
x^4+x^4=2
x=y= $$\pm1$$
max= 1+1=2 @ $$\left(1,1\right)$$ and $$\left(-1,-1\right)$$

I don't know how to find the min and not sure about the max above
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited: Mar 22, 2009
2. Mar 22, 2009

### HallsofIvy

Re: optimization

My recomendation is that you go back and read the problem carefully! What you have written here makes no sense. Usually you use Lagrange multiplier method maximize or minimize a function subject to some constraint. You have two functions with no constraint. Is one of those, either f or g, supposed to be equal to a number?

3. Mar 22, 2009

### tinkus

Re: optimization

yes the constraint function is incorrect, i ommitted =2

4. Mar 22, 2009

### HallsofIvy

Re: optimization

You have found that y2= x2 and you know that $x^4+ y^4= 2$. That tells you that $x= \pm 1$ and $x= \pm 1$. That gives you four possible points: (1, 1), (-1, -1), (1, -1), and (-1, 1). You might want to consider whether there are both maximum and mimimum values.

5. Mar 22, 2009

### tinkus

Re: optimization

the points all equal 2(max). i still need to find the min which according to the answer key is sqrt2, I don't know how to get that.