1. Homework Statement [/b]

f[tex]\left(x,y\right)[/tex] = x^2 +y^2

g[tex]\left(x,y\right)[/tex] = x^4+y^4 = 2

Find the maximum and minimum using Lagrange multiplier

grad f = 2xi +2yj

grad g= 4x^3i + 4y^3j

grad f= λ grad g

2x=4x^3λ and 2y= 4y^3λ

2x^2 = 2y^2

x^2=y^2

x= [tex]\pm[/tex]y

x^4+x^4=2

x=y= [tex]\pm1[/tex]

max= 1+1=2 @ [tex]\left(1,1\right)[/tex] and [tex]\left(-1,-1\right)[/tex]

I don't know how to find the min and not sure about the max above

f[tex]\left(x,y\right)[/tex] = x^2 +y^2

g[tex]\left(x,y\right)[/tex] = x^4+y^4 = 2

Find the maximum and minimum using Lagrange multiplier

**2. Homework Equations****3. The Attempt at a Solution**grad f = 2xi +2yj

grad g= 4x^3i + 4y^3j

grad f= λ grad g

2x=4x^3λ and 2y= 4y^3λ

2x^2 = 2y^2

x^2=y^2

x= [tex]\pm[/tex]y

x^4+x^4=2

x=y= [tex]\pm1[/tex]

max= 1+1=2 @ [tex]\left(1,1\right)[/tex] and [tex]\left(-1,-1\right)[/tex]

I don't know how to find the min and not sure about the max above

**1. Homework Statement****2. Homework Equations****3. The Attempt at a Solution****1. Homework Statement****2. Homework Equations****3. The Attempt at a Solution****1. Homework Statement****2. Homework Equations****3. The Attempt at a Solution****1. Homework Statement****2. Homework Equations****3. The Attempt at a Solution**
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