Let $f ( x , y ) = k x ^ { 3 } - 3 k x + y ^ { 2 }$

question 60

Essay

Let $f ( x , y ) = k x ^ { 3 } - 3 k x + y ^ { 2 }$ where k $\neq$ 0.Determine the values of k (if any)for which the critical point at (-1, 0)is a local minimum.

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Definitions:

Price of X

The amount of money required to purchase a unit of good X in the market.

Utility Function

A mathematical model in economics that represents how different goods or outcomes give varying levels of satisfaction or happiness to an individual.

Price of Leather Jackets

The price of leather jackets refers to the amount of money required to purchase a leather jacket, which may vary based on quality, brand, and market.

Demand

The quantity of a good or service that consumers are willing and able to purchase at various prices.