JEE Math Practice Question

Let $$a,b \in R$$ be such that the function $$f$$ given by $$f\left( x \right) = In\left| x \right| + b{x^2} + ax,\,x \ne 0$$ has extreme values at $$x=-1$$ and $$x=2$$ Statement-1 : $$f$$ has local maximum at $$x=-1$$ and at $$x=2$$. Statement-2 : $$a = {1 \over 2}$$ and $$b = {-1 \over 4}$$

1. A.Statement - 1 is false, Statement - 2 is true.
2. B.Statement - 1 is true , Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1.
3. C.Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1.
4. D.Statement - 1 is true, Statement - 2 is false.