A Function and Its Graph Are Given $y = f ( x )$

Multiple Choice

A function and its graph are given. Use the second derivative to locate all x-values of points of inflection on the graph of $y = f ( x )$ . Check these results against the graph shown. $$y = 18 x ^ { 4 } - 54 x ^ { 2 } + 36$$

A) $x = - \frac { \sqrt { 2 } } { 2 }$
B) $x = 0$
C) $x = \frac { \sqrt { 2 } } { 2 }$
D) $x = \frac { \sqrt { 2 } } { 2 }$ , $x = - \frac { \sqrt { 2 } } { 2 }$
E) $x = - \frac { \sqrt { 2 } } { 2 }$ , $x = 0$ , $x = - \frac { \sqrt { 2 } } { 2 }$