Find the Maximum and Minimum Values of the Function $f ( x , y ) = x ^ { 2 } + 6 x y + y ^ { 2 }$

question 44

Short Answer

Find the maximum and minimum values of the function $f ( x , y ) = x ^ { 2 } + 6 x y + y ^ { 2 }$ subject to the constraint $x ^ { 2 } + y ^ { 2 } \leq 32$ .

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Definitions:

Defensive Self-Esteem

A psychological condition where an individual's self-esteem is formed from defending oneself against criticisms, leading to fragile self-confidence.

Boast

To speak with excessive pride and self-satisfaction about one's achievements, possessions, or abilities.

Criticizes

The act of expressing disapproval or finding faults in something or someone, often with the intention of suggesting possible improvements.

Factor Analysis

A statistical method used to identify underlying variables, or factors, that explain the pattern of correlations among multiple observed measures.