If \( x=-1 \) and \( x=2 \) are extreme points of \( f(x)=\alpha \log |x|+\beta x^{2}+x \), then...
If \( x=-1 \) and \( x=2 \) are extreme points of \( f(x)=\alpha \log |x|+\beta x^{2}+x \), then
[2014 JEE Main]
(a) \( \alpha=-6, \beta=\frac{1}{2} \)
(b) \( \alpha=-6, \beta=-\frac{1}{2} \)
(c) \( \alpha=2, \beta=-\frac{1}{2} \)
(d) \( \alpha=2, \beta=\frac{1}{2} \)
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