Determine Where the Graph of the Function $f ( x ) = x ^ { 3 } - 6 x$

question 3

Multiple Choice

Determine where the graph of the function $f ( x ) = x ^ { 3 } - 6 x$ is concave upward and where it is concave downward. Also, find all inflection points of the function.

• A) \(\mathrm { CU }\) on \(( \sqrt { 2 } , \infty ) , \mathrm { CD }\) on \(( - \infty , \sqrt { 2 } )\),
• IP \(( \sqrt { 2 } , - 4 \sqrt { 2 } )\)
• B) \(\mathrm { CU }\) on \(( - \sqrt { 2 } , \sqrt { 2 } ) , \mathrm { CD }\) on \(( - \infty , - \sqrt { 2 } )\) and \(( \sqrt { 2 } , \infty )\)
• IP \(( - \sqrt { 2 } , 4 \sqrt { 2 } )\) and \(( \sqrt { 2 } , - 4 \sqrt { 2 } )\)
• C) \(\mathrm { CU }\) on \(( 0 , \infty ) , \mathrm { CD }\) on \(( - \infty , 0 )\),
• IP \(( 0,0 )\)
• D) \(\mathrm { CU }\) on \(( - \sqrt { 2 } , \infty ) , \mathrm { CD }\) on \(( - \infty , - \sqrt { 2 } )\),
• IP \(( - \sqrt { 2 } , 4 \sqrt { 2 } )\)

---

Definitions:

Operations

Activities involved in the day-to-day running of a business for the purpose of producing value for the stakeholders.

Raw Materials

The basic materials and components used at the start of the production process, essential for creating the finished product.

Inventories

Quantifiable goods or materials that a business holds for the purpose of sale in the ordinary course of business, production, or use.

Job-Order Costing

A cost accounting system that collects costs individually for each job, suitable for customized orders or distinctly identifiable products.