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.
- $$f ( x , y ) = x y , \quad x ^ { 2 } + y ^ { 2 } = 32$$

A) Maximum: 16 at (4, 4) ; minimum: -16 at (-4, -4)
B) Maximum: 16 at (4, -4) and (-4, 4) ; minimum: -16 at (4, 4) and (-4, -4)
C) Maximum: 16 at (4, 4) and (-4, -4) ; minimum: -16 at (4, -4) and (-4, 4)
D) Maximum: 16 at (4, 4) ; minimum: 0 at (0, 0)