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

question 142

Multiple Choice

Find the absolute maxima and minima of the function on the given domain.
- $$f ( x , y ) = 5 x y ^ { 2 } + 8 x y \quad \text { on the trapezoidal region with vertices } ( 0,0 ) , ( 1,0 ) , ( 0,2 ) \text {, and } ( 1,1 )$$

• A) Absolute maximum: 16 at (0, 2); absolute minimum: 0 at (0, 0)
• B) Absolute maximum: 10 at (2, 0); absolute minimum: 5 at (1, 0)
• C) Absolute maximum: 13 at (1, 1); absolute minimum: 5 at (1, 0)
• D) Absolute maximum: 13 at (1, 1); absolute minimum: 0 at (0, 0)