Identify the Vertex and Determine the Minimum or Maximum Value $$f ( x ) = - 2 ( x - 4 ) ^ { 2 } + 7$$

question 229

Multiple Choice

Identify the vertex and determine the minimum or maximum value of the function.
- $$f ( x ) = - 2 ( x - 4 ) ^ { 2 } + 7$$

• A) Vertex: \(( 4,7 )\)
• Maximum: 7
• B) Vertex: \(( 4,7 )\)
• Minimum: 7
• C) Vertex: \(( 4 , - 7 )\)
• Minimum: -7
• D) Vertex: \(( 4 , - 7 )\)
• Maximum: -7

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Definitions:

Pure Monopolist's Demand Curve

A graphical representation showing how a monopolist's quantity sold varies with price, typically downward sloping, reflecting that the monopolist can set prices above marginal costs.

Elastic

A characteristic of a good or service indicating that its demand or supply is sensitive to changes in price.

Marginal Revenue

The additional revenue that a firm receives from selling one more unit of a good or service.

Pure Monopolist

A single seller in a market with no close substitutes for the product or service offered, leading to significant control over prices and market conditions.