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.
- $$f ( x , y , z ) = ( x - 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } + ( z - 2 ) ^ { 2 } , x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 36$$

A) Maximum: 81 at (-2, -4, -4) ; minimum: 9 at (2, 4, 4)
B) Maximum: 49 at (-2, 4, -4) ; minimum: 41 at (2, -4, 4)
C) Maximum: 77 at (-4, -4, -2) ; minimum: 13 at (4, 4, 2)
D) Maximum: 77 at (-4, -2, -4) ; minimum: 13 at (4, 2, 4)