Let a, b R be such that the function f given by `f(x)""=""ln""|x|""+""b x^2+""a x ,""x!=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""=1/2"and"b=(-1)/4` (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Explanation

`f(x) = ln|x| + bx^2 + ax`

`f'(x) = 1/x + 2bx + a= 0`

when x=-1;`-1 - 2b + a=0`

`a= 2b +1`

& when x=2 ; `1/2 + 4b + a = 0`

`a=-4b -1/2`

eqn`(1) - (2)`

`6b + 3/2 = 0`

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