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

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