- #1
BeBattey
- 59
- 6
Homework Statement
Maximize f(x,y,z)=x[tex]^{2}[/tex]+y[tex]^{2}[/tex]+z[tex]^{2}[/tex] with constraint x[tex]^{4}[/tex]+y[tex]^{4}[/tex]+z[tex]^{4}[/tex]=1 using Lagrange multipliers
The Attempt at a Solution
I've got the setup as:
[tex]\Lambda[/tex](x,y,z,[tex]\lambda[/tex])=x[tex]^{2}[/tex]+y[tex]^{2}[/tex]+z[tex]^{2}[/tex]+[tex]\lambda[/tex]x[tex]^{4}[/tex]+[tex]\lambda[/tex]y[tex]^{4}[/tex]+[tex]\lambda[/tex]z[tex]^{4}[/tex]+[tex]\lambda[/tex]
I solve for all partials nice and clean, and spit out [tex]\sqrt{3}[/tex] as the minimum value fine, with x=y=z=sqrt(6)/4 but I can't for the life of my find out how the max is 1.
Any and all help, even direction greatly appreciated.