Let $a, b \in R$ be such that the function $f$ given by $f(x) = In \; |x| + bx^2 + ax, \; \; x \neq 0$ has extreme values at $x = -1$ and $x = 2$ <br> Statement 1 : $f$ has focal maximum at $x = -1$ and at $x = 2$ <br> Statement 2 : $a = \frac{1}{2}$ and $b = \frac{-1}{4}$

Question

( A ) Statement 1 is true, statement 2 is false
( B ) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
( C ) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
( D ) Statement 1 is false, statement 2 is true