### Using Lagrange Multipliers to Find Extreme Values

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.