Find the Absolute Maxima and Minima of the Function on the Given

Multiple Choice

Find the absolute maxima and minima of the function on the given domain.
- $$f ( x , y ) = x ^ { 2 } + y ^ { 2 } \text { on the diamond-shaped region } | x | + | y | \leq 4$$

A) Absolute maximum: 16 at (4, 0) , (-4, 0) , (0, 4) , and (0, -4) ; absolute minimum: 0 at (0, 0)
B) Absolute maximum: 8 at 2, 2 , 2, - 2 , - 2, 2 , and - 2, - 2 ; absolute minimum: 0 at (0, 0)
C) Absolute maximum: 16 at (4, 0) and (0, 4) ; absolute minimum: 0 at (-4, 0) and (0, -4)
D) Absolute maximum: 16 at (4, 0) , (-4, 0) , (0, 4) , and (0, -4) ; absolute minimum: 8 at 2, 2 , 2, - 2 , - 2, 2 , and - 2, - 2 ,