Find the Maximum and Minimum Values Of $f ( x , y ) = x ^ { 2 } + 7 x y + y ^ { 2 }$

question 7

Essay

Find the maximum and minimum values of $f ( x , y ) = x ^ { 2 } + 7 x y + y ^ { 2 }$ subject to the constraint $x ^ { 2 } + y ^ { 2 } = c$ , with $c > 0$ .Your answers may depend on c.

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Definitions:

Integer

A whole number that can be positive, negative, or zero, not including fractions or decimals.

Currency Format

A way of displaying numbers in a specific monetary style, which includes symbols, decimal places, and digit grouping according to different cultural norms.

Number Field

A data field specifically designed to hold numeric values, often used in databases and form inputs.

Currency Symbol

A graphical sign used as a shorthand for a currency's name, especially in reference to amounts of money.