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 \(( - \sqrt { 2 } , 4 \sqrt { 2 } )\)

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