Determine Where the Function Is Increasing and Where It Is $$f ( x ) = - x ^ { 2 } - 2 x + 8$$

question 130

Multiple Choice

Determine where the function is increasing and where it is decreasing.
- $$f ( x ) = - x ^ { 2 } - 2 x + 8$$

• A) increasing on \(( - \infty , - 1 )\)
• decreasing on \(( - 1 , \infty )\)
• B) increasing on \(( - 1 , \infty )\)
• decreasing on \(( - \infty , - 1 )\)
• C) increasing on \(( 9 , \infty )\)
• decreasing on \(( - \infty , 9 )\)
• D) increasing on \(( - \infty , 9 )\)
• decreasing on \(( 9 , \infty )\)

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Definitions:

Initial Endowment

The set of resources or assets that agents possess at the start of an economic analysis or experiment.

Pareto Optimal

A scenario in resource distribution where enhancing the welfare of a single person would lead to a detriment to another person.

Utility Function

A mathematical representation that ranks an individual's preferences for various outcomes, reflecting the level of satisfaction or happiness that different bundles of goods and services provide to the individual.

Edgeworth Box

A diagram used in economics to show the distribution of resources and the potential for Pareto improvements within an exchange economy.