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

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