Find the Points of Inflection and Discuss the Concavity of the Function

question 121

Multiple Choice

Find the points of inflection and discuss the concavity of the function. $f ( x ) = 4 x ^ { 3 } - 5 x ^ { 2 } + 5 x - 7$

• A) inflection point at \(x = - \frac { 5 } { 12 } ;\) concave upward on \(\left( - \infty , - \frac { 5 } { 12 } \right)\); concave downward on \(\left( - \frac { 5 } { 12 } , \infty \right)\)
• B) inflection point at \(x = \frac { 5 } { 24 }\); concare downward on \(\left( - \infty , \frac { 5 } { 24 } \right) ;\) concave upward on \(\left( \frac { 5 } { 24 } , \infty \right)\)
• C) inflection point at \(x = \frac { 5 } { 12 } ;\) concave downward on \(\left( - \infty , \frac { 5 } { 12 } \right)\); concave upward on \(\left( \frac { 5 } { 12 } , \infty \right)\)
• D) inflection point at \(x = - \frac { 5 } { 12 } ;\) concave downward on \(\left( - \infty , - \frac { 5 } { 12 } \right)\); concave upward on \(\left( - \frac { 5 } { 12 } , \infty \right)\)
• E) inflection point at \(x = \frac { 5 } { 12 }\); concave upward on \(\left( - \infty , \frac { 5 } { 12 } \right)\); concave downward on \(\left( \frac { 5 } { 12 } , \infty \right)\)

---

Definitions:

Long-Term Assets

Assets owned by a company that have a useful life of more than one year, such as property, plant, and equipment.

Current Assets

Current assets are assets that are expected to be converted into cash, sold or consumed within a year or within the normal operating cycle of the business, such as cash, inventory, and receivables.

Installation

refers to the process of setting up and configuring equipment or software to make it ready for use.

Repairs

Expenditures to restore or maintain an asset in its normal operating condition without significantly improving its life or value.