Multivariable Help:
Once again I'm stumbling on Lagrange Multipliers. I need to find the maximum and minimum distance from the origin of a point on the ellipsoid 4x^2 + (y-2)^2 + (z-1)^2 = 4.
I've determined that the partials are as follows:
df/dx = 2x
df/dy = 2y
df/dz = 2z
dg/dx = 8x
dg/dy = 2(y-2)
dg/dz = 2(z-1)
From this, I get the Lagrange equations to be:
2x = L(8x)
2y = L(2y-4)
2z = L(2z-2)
From these equations, I get x = 0, L = 1/4, y = -2/3 and z = -1/3. Where do I go from here?

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Oh my... *Pythagoras

ok for that I get sqrt(5)/3. Now how do I get the farthest point?

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