$f(x) = ax^2 + bx$ has a local maximum value 8 at $x = 2$. What is $b$?

Explanation

1. 01

   $f'(2) = 4a + b = 0$ and $f(2) = 4a + 2b = 8$.

2. 02

   From the first, $b = -4a$; then $4a - 8a = 8$ gives $a = -2$ and $b = 8$.