Use Lagrange Multipliers to find the maximum and minimum values of f(x,y)=x[tex]^{2}[/tex]y subject to the constraint g(x,y)=x[tex]^{2}[/tex]+y[tex]^{2}[/tex]=1.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\nabla[/tex]f=[tex]\lambda[/tex][tex]\nabla[/tex]g

[tex]\nabla[/tex]f=<2xy,x[tex]^{2}[/tex]>

[tex]\nabla[/tex]g=<2x,2y>

1: 2xy=2x[tex]\lambda[/tex] ends up being y=[tex]\lambda[/tex]

2: x[tex]^{2}[/tex]=2y[tex]\lambda[/tex] ends up being(1 into 2) x=[tex]\sqrt{2\lambda[/tex] ^{2}}[/tex]

3: x[tex]^{2}[/tex]+y[tex]^{2}[/tex]=1

1 and 2 into 3:

(2[tex]\lambda[/tex][tex]^{2}[/tex])+([tex]\lambda[/tex][tex]^{2}[/tex])=1

Do I then solve for [tex]\lambda[/tex] and x and y? Did I do the above correctly? I am going off of an example of f(x,y,z) so I'm not sure if I'm correct. Any help is greatly appreciated!

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# Homework Help: Lagrange Multiplier

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