Use Lagrange multipliers to find maximum and minimum values of the function subject to a given constraint or constraints.
1.) f(x,y,z)= xyz; x^2 + 2y^2 + 3z^2 = 6
2.) f(x,y,z)= x^2 + y^2 + z^2; x^4 + y^4 + z^4 = 1
3.) f(x,y,z)= x^4 + y^4 + z^4; x^2 + y^2 + z^2 = 1