If $x = -1$ and $x = 2$ are extreme points of $f(x) = \alpha \log |x| + \beta x^2 + x$, then

Question

( A ) $\alpha = -6, \beta = \frac{1}{2}$
( B ) $\alpha = -6, \beta = -\frac{1}{2}$
( C ) $\alpha = 2, \beta = -\frac{1}{2}$
( D ) $\alpha = 2, \beta = \frac{1}{2}$