For a real number $a$ ($a > 1$), define the function $f ( x )$ as
$$f ( x ) = ( x + 1 ) ( x - 1 ) ( x - a)$$
Define the function
$$g ( x ) = x ^ { 2 } \int _ { 0 } ^ { x } f ( t ) d t - \int _ { 0 } ^ { x } t ^ { 2 } f ( t ) d t$$
such that $g ( x )$ has exactly one extremum. What is the maximum value of $a$? [4 points]\\
(1) $\frac { 9 \sqrt { 2 } } { 8 }$\\
(2) $\frac { 3 \sqrt { 6 } } { 4 }$\\
(3) $\frac { 3 \sqrt { 2 } } { 2 }$\\
(4) $\sqrt { 6 }$\\
(5) $2 \sqrt { 2 }$