(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the points on the ellipse x^{2}+ 2y^{2}= 1 where f(x,y) = xy has its extreme values.

2. Relevant equations

3. The attempt at a solution

f(x,y,z) = x^{2}+ y^{2}+ z^{2}-- constraint

g(x,y,z) = x^{2}+ 2y^{2}-1 = 0

gradient of f = [tex]\lambda[/tex] * gradient of g

2xi + 2yj + 2zk = [tex]\lambda[/tex]2xi + [tex]\lambda[/tex]4yj

2x = [tex]\lambda[/tex]2x

2y = [tex]\lambda[/tex]4y

2z = 0

I don't know where to go from here, can someone help me out?

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# Homework Help: Lagrange Multipliers with ellipse

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