Find the Local Maximum and Minimum Values and Saddle Points $f ( x , y ) = 2 x ^ { 3 } + 4 y ^ { 3 } + 3 x ^ { 2 } - 12 x - 192 y + 5$

question 52

Essay

Find the local maximum and minimum values and saddle points of the function $f ( x , y ) = 2 x ^ { 3 } + 4 y ^ { 3 } + 3 x ^ { 2 } - 12 x - 192 y + 5$ .

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Definitions:

Satisfy Customer Needs

The process of meeting or exceeding customer expectations to encourage loyalty and repeat business.

Monetary Outlay

The amount of money spent on a specific item, service, or activity.

Measure

A method or tool used to quantify or assess a variable or condition.

Value

Refers to the importance or worth that a product or service has in the eyes of the consumer, often influencing their purchasing decisions.