The function $f ( x ) = 2 x ^ { 3 } - 9 x ^ { 2 } + a x + 5$ has a local maximum at $x = 1$ and a local minimum at $x = b$. What is the value of $a + b$? (Here, $a$ and $b$ are constants.) [3 points] (1) 12 (2) 14 (3) 16 (4) 18 (5) 20
The function $f ( x ) = 2 x ^ { 3 } - 9 x ^ { 2 } + a x + 5$ has a local maximum at $x = 1$ and a local minimum at $x = b$. What is the value of $a + b$? (Here, $a$ and $b$ are constants.) [3 points]\\
(1) 12\\
(2) 14\\
(3) 16\\
(4) 18\\
(5) 20