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

question 37

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) \(\operatorname { CU }\) on \(( - \sqrt { 2 } , \infty ) , \mathrm { CD }\) on \(( - \infty , - \sqrt { 2 } )\),
• IP \(( - \sqrt { 2 } , 4 \sqrt { 2 } )\)

Understand the role and implementation of data warehouses and data marts in decision-making processes.

Realize the importance of knowledge management and intellectual capital in leveraging organizational performance.

Understand and calculate the payback period for investment projects.

Identify and evaluate the profitability index and internal rate of return as investment appraisal methods.

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Definitions:

Outstanding Deposit

Funds that have been received but not yet processed by a financial institution.

Bank Statement Balance

The total amount of money that is available in a bank account at a particular point in time, as recorded by the bank.

Checkbook Balance

The current total amount of funds available in a checking account, reflecting all transactions that have been recorded in the checkbook ledger.

Bank Error

A mistake made by a bank in accounting transactions, deposits, withdrawals, or charges.