Find the Critical Number(s) (If Any) and Test Them to Determine

question 190

Essay

Find the critical number(s) (if any) and test them to determine if $f ( x ) = 3 x ^ { 4 } - 8 x ^ { 3 } + 9$ has a local maximum or local minimum or neither at each critical number.

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Definitions:

Private Consumption

The total value of all goods and services consumed by private households.

Pareto Efficient

An economic state where resources are allocated in a way that it is impossible to make any one individual better off without making at least one individual worse off.

Public Good

A commodity or service that is provided without profit to all members of a society, either by the government or a private individual or organization.

Private Good

An economic product or service that is consumed by an individual or a specific group, characterized by its exclusivity and rivalry in consumption.