Find the Direction in Which the Function $f ( x , y ) = x ^ { 4 } y - x ^ { 3 } y ^ { 2 }$

question 23

Short Answer

Find the direction in which the function $f ( x , y ) = x ^ { 4 } y - x ^ { 3 } y ^ { 2 }$ decreases fastest at the point $( 2 , - 1 )$ .

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Definitions:

Income

Money that an individual or business receives in exchange for providing a good or service or through investing capital.

Substitutes

are goods or services that can be used in place of each other, where an increase in the price of one leads to an increase in demand for the other.

Demand Curve

A graph showing the relationship between the quantity of a good or service that consumers are willing to buy and its price.

Price

The pecuniary sum needed, anticipated, or disbursed for purchasing something.