Decide, using Lagrange multiplier, the extremes for
I've tried, but I just couldn't solve the system of equations that arise. Maybe it's z^3 that confuses me.
We are asked to used Lagrange multipliers to find the extrema for:
subject to the constraint:
By the theorem of Lagrange, we need to solve the system:
These two equations imply:
Substituting for y into the constraint yields:
Hence, the extrema occur at: