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Homework Statement
Find the points on the ellipse x2 + 2y2 = 1 where f(x,y) = xy has its extreme values.
Homework Equations
The Attempt at a Solution
f(x,y,z) = x2 + y2 + z2 -- constraint
g(x,y,z) = x2 + 2y2 -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?