Find the extreme values of the function subject to the given constraint.
-$$f ( x , y , z ) = x + 2 y - 2 z , \quad x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 9$$
A) Maximum: 1 at (-1, -2, -3); minimum: -1 at (1, 2, 3)
B) Maximum: 1 at (1, -2, -2); minimum: -1 at (-1, 2, 2)
C) Maximum: 8 at (2, 1, -2); minimum: -8 at (-2, -1, 2)
D) Maximum: 9 at (1, 2, -2); minimum: -9 at (-1, -2, 2)

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The Answer of Find the extreme values of the function subject to the given constraint.
-$$f ( x , y , z ) = x + 2 y - 2 z , \quad x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 9$$
A) Maximum: 1 at (-1, -2, -3); minimum: -1 at (1, 2, 3)
B) Maximum: 1 at (1, -2, -2); minimum: -1 at (-1, 2, 2)
C) Maximum: 8 at (2, 1, -2); minimum: -8 at (-2, -1, 2)
D) Maximum: 9 at (1, 2, -2); minimum: -9 at (-1, -2, 2)

Find the Extreme Values of the Function Subject to the Given