- #1
tinkus
- 13
- 0
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
Homework Equations
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
Last edited: