Determine Where the Graph of the Function $f ( x ) = 9 x - \sqrt { 4 - x ^ { 2 } }$

question 138

Multiple Choice

Determine where the graph of the function $f ( x ) = 9 x - \sqrt { 4 - x ^ { 2 } }$ is concave upward and where it is concave downward. Also, find all inflection points of the function. Select the correct answer.

• A) \(\mathrm { CU }\) on \(( - 2,2 )\),
• IP none
• B) \(\mathrm { CU }\) on \(( - \infty , - 2 )\) and \(( 2 , \infty ) , \mathrm { CD }\) on \(( - 2,2 )\),
• IP \(( - 2 , - 18 )\) and \(( 2,18 )\)
• C) \(\mathrm { CD }\) on \(( - 2,2 )\),
• IP none
• D) \(\mathrm { CU }\) on \(( - 2,2 ) , \mathrm { CD }\) on \(( - \infty , - 2 )\) and \(( 2 , \infty )\),
• IP \(( - 2 , - 18 )\) and \(( 2,18 )\)

---

Definitions:

Kinked Demand Curve

A concept in economics describing a situation where a firm's demand curve has a distinct kink due to competitors only matching price increases but not price decreases, leading to price rigidity.

Marginal Cost

The extra expense associated with the production of an additional unit of a product or service.

Kinked Demand Curve Model

A model in economics illustrating how firms in oligopoly markets might maintain stable prices despite changes in cost or demand, due to the asymmetric responses of rivals to price changes.

Price Reduction

A decrease in the selling price of goods or services, often to attract more buyers or respond to market conditions.