Use Lagrange Multipliers to Find the Maximum and the Minimum $f ( x , y ) = x y z ; \quad x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 15$

Short Answer

Use Lagrange multipliers to find the maximum and the minimum of f subject to the given constraint(s). $f ( x , y ) = x y z ; \quad x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 15$