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I am doing this lagrange multiplier problem with 2 constraints. I have completely solved it as shown in the image below. I have found that for lambda = 1 and mu = +/- 1/2 I have that x=+/- [sqrt(2)] y=+/- [1/sqrt(2)] and z=+/- [1/sqrt(2)].

So I am trying to figure out what points I actually have now. It seemed to me that since for x,y,z I have both a positive and negative value, I should have 2*2*2= 8 points to look at. But the solution only lists four. Am I messing this up somehow? Are there not 8 points given by the solution below? Thanks.

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# Homework Help: Lagrange Multiplier MethodMaking Sense of the Results

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