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

$\begin{array}{1 1}(A)\;\alpha =-6, \beta=\large\frac{1}{2} \\ (B)\;\alpha =-6, \beta=\large\frac{-1}{2} \\(C)\;\alpha =2, \beta=\large\frac{-1}{2} \\(D)\;\alpha =2, \beta=\large\frac{1}{2} \end{array}$

$\alpha =2, \beta=\large\frac{-1}{2}$ is correct.
Hence C is the correct answer.