Find the Extreme Values of the Function Subject to the Given

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $$f ( x , y , z ) = x ^ { 3 } + y ^ { 3 } + z ^ { 3 } , x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$$

A) Maximum: 8 at (2, 0, 0) , (0, 2, 0) , (0, 0, 2) ; minimum: 0 at (0, 0, 0)
B) Maximum: 8 at (2, 0, 0) ; minimum: 0 at (0, 0, 0)
C) Maximum: 8 at (2, 0, 0) , (0, 2, 0) , (0, 0, 2) ; minimum: -8 at (-2, 0, 0) , (0, -2, 0) , (0, 0, -2)
D) Maximum: 8 at (2, 0, 0) ; minimum: -8 at (-2, 0, 0)