Consider the Function $f ( x , y ) = x ^ { 4 } + 2 x ^ { 3 } y - 6 x ^ { 2 } y ^ { 2 } + 7 x y ^ { 3 } - y ^ { 4 } + 3$

question 39

Short Answer

Consider the function $f ( x , y ) = x ^ { 4 } + 2 x ^ { 3 } y - 6 x ^ { 2 } y ^ { 2 } + 7 x y ^ { 3 } - y ^ { 4 } + 3$ Check that (0,0)is a critical point of f and classify it as a local minimum, local maximum or saddle point.

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Definitions:

Fixed Costs

Expenses that do not change with the level of production or sales in the short term, such as rent, salaries, or insurance premiums.

Unitised

Refers to the conversion of a product or service into quantifiable units, typically for ease of calculation, tracking, or comparison.

Special Decisions

Decisions made in unique or non-recurring situations requiring specific analysis or responses.

Annual Operating Costs

The total expenses associated with the day-to-day functioning of a business or project over one year.