Find the maximum value of the real number $a$ such that the function $f ( x ) = x ^ { 3 } + a x ^ { 2 } - \left( a ^ { 2 } - 8 a \right) x + 3$ is increasing on the entire set of real numbers. [3 points]
Find the maximum value of the real number $a$ such that the function $f ( x ) = x ^ { 3 } + a x ^ { 2 } - \left( a ^ { 2 } - 8 a \right) x + 3$ is increasing on the entire set of real numbers. [3 points]