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- Homework Statement
- find the max of f=xyz on the domain bounded by the unit sphere in R3 and x+y+z=0

- Relevant Equations
- xyz

x^2 + y^2 + z^2 = 1

x+y+z=0

I tried parametrizing the domain using spherical coordinates, with theta and phi.

I also tried the method of lagrange multipliers, but the substitutions don't easily result in an easy solution. It requires solving five equations for five variables, and no easy way to isolate variables.

I think the hint is pointing at the fact the domain is a circle of radius 1 centered at the origin.

graph of the domain is the intersection of the green plane and the hollow red sphere.

Any help would be appreciated. thank you.

I also tried the method of lagrange multipliers, but the substitutions don't easily result in an easy solution. It requires solving five equations for five variables, and no easy way to isolate variables.

I think the hint is pointing at the fact the domain is a circle of radius 1 centered at the origin.

graph of the domain is the intersection of the green plane and the hollow red sphere.

Any help would be appreciated. thank you.

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