The function $f ( x ) = 2 x ^ { 3 } - 12 x ^ { 2 } + a x - 4$ has a local maximum value $M$ at $x = 1$. Find the value of $a + M$. (Here, $a$ is a constant.) [3 points]
The function $f ( x ) = 2 x ^ { 3 } - 12 x ^ { 2 } + a x - 4$ has a local maximum value $M$ at $x = 1$. Find the value of $a + M$. (Here, $a$ is a constant.) [3 points]