Find extreme values for function of 3 variables and two constraints

[jimbo71]

Homework Statement

see problem 7 attachement

Homework Equations

The Attempt at a Solution

see problem 7 attempt attachment
I found the fgrad and ggrad and hgrad. I set fgrad equal to lambda*ggrad+mu*hgrad. using the two constraint equations I was able to solve for x,y,z,lambda,mu. However again I am not sure what to do with these values. Also in this problem is states find the extreme values. does that mean I need to find MIN and MAX. and if so how do i do that. Also can someone please check to see if my algebra is correct in solving for x,y,z,lamdba,mu. Thank you

 

[jimbo71]

i need help asap