Not sure what I'm doing wrong here.....when I put into wolfram, it said the answer was (1,1,sqrt(2))
Find the extreme values of
f(x,y,z)=xyz
x^2+y^2+z^2=4
g1=x^2+y^2+z^2-4
x+y=2
g2=x+y-2
so I took the gradient of the function to get:
grad f=(yz)i+(xz)j+(xy)k
grad g1=(2x)i+(2y)j+(2z)k
grad g2=i+j
grad f=λgrad g1+μgrad g2
(yz)i+(xz)j+(xy)k=(2xλ+μ)i+(2xλ+μ)j+(2zλ)k