- #1
Ready2GoXtr
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Homework Statement
Minimize xyz on the unit sphere x2+y2+z2=1
Homework Equations
Lagrange Method.
The Attempt at a Solution
My attempt so far.. I am trying to follow the lagrange method
I set f(x,y,z)=xyz and g(x,y,z)=x2+y2+z2-1
g(x,y,z) = 0
I took the gradient of both functions
Δf(x,y,z) = (yz)i + (xz)j + (xy)k Δg(x,y,z) = (2x)i + (2y)j + (2z)k
Then set Δf(x,y,z) = λΔg(x,y,z)
Giving me the following
yz = λ2x
xz = λ2y
xy = λ2z
After that i am not sure what to do. Please help.