Question

Find the locations of the points with minimum distance to x^4yz^4 = 8√2 to the origin.

Answer 1

you function would be:
\(f(x,y,z)=x^2+y^2+z^2\)
constraint:
\(x^4yz^4 - 8√2=0\)
Using Lagrange multipliers:
\(df+\lambda dg=0\)
You will get a system with 4 equations and four unknowns. Solve it and later check either it gives you mínimum or maximum

Answer 2

Forgot to say what g is: g(x,y,z)=x^4yz^4 -8√2