Let $a, b \in \mathbb{R}$ be such that the function $f$ given by $f(x) = \ln|x| + bx^{2} + ax$, $x \neq 0$ 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) Statement 1 is false, Statement 2 is true (2) Statement 1 is true, Statement 2 is false (3) Statement 1 is true, Statement 2 is the correct explanation for Statement 1 (4) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1
Let $a, b \in \mathbb{R}$ be such that the function $f$ given by $f(x) = \ln|x| + bx^{2} + ax$, $x \neq 0$ 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) Statement 1 is false, Statement 2 is true\\
(2) Statement 1 is true, Statement 2 is false\\
(3) Statement 1 is true, Statement 2 is the correct explanation for Statement 1\\
(4) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1