Find the Absolute Maximum and Minimum Values Of $f ( x , y ) = x ^ { 2 } + 2 x y + 3 y ^ { 2 }$

question 132

Essay

Find the absolute maximum and minimum values of $f ( x , y ) = x ^ { 2 } + 2 x y + 3 y ^ { 2 }$ over the region $D$ , where $D$ is a closed triangular region with vertices $( - 1 , - 2 )$ , $( - 1,1 )$ , and $( 2,1 )$ .

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Definitions:

Passions

Intense, driving, or overwhelming feelings or emotions that significantly influence human behavior and decision-making.

Misperceive

To perceive incorrectly; to misunderstand or to have a mistaken interpretation of something.

Clear Thinking

The process of thinking in a clear, logical, and coherent manner, often involving critical analysis and reasoning.

Identity Theory

A view in the philosophy of mind which holds that mental states and processes are identical to brain states and processes.