Find the Maximum Value of F (X, Y, Z) = $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 12$

Multiple Choice

Find the maximum value of f (x, y, z) = xyz on the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 12$ .

A) 8
B) $8 \sqrt { 3 }$
C) 16
D) No maximum, unbounded