Find the Local Maximum and Minimum Values and Saddle Points $f ( x , y ) = 3 x ^ { 3 } + y ^ { 2 } - 9 x + 4 y$

question 263

Essay

Find the local maximum and minimum values and saddle points of the function $f ( x , y ) = 3 x ^ { 3 } + y ^ { 2 } - 9 x + 4 y$ .

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Definitions:

Substitute Good

A product or service that consumers can use in place of another product or service, often when prices rise or the original becomes unavailable.

Wood Pulp

A material prepared from wood by a chemical or mechanical process used in the production of paper and cellulose products.

Quantity Supplied

The amount of a good or service that producers are willing and able to sell at a given price within a specified time period.

Quantity Demanded

the total amount of a good or service that consumers are willing and able to purchase at a given price in a specified period.