If `f(x)=alog|x|+b x^2+x` has its extremum values at `x=-1a n dx=2,` then `a=2,b=-1` `a=2,b=-1//2` `a=-2,b=1//2` (d) none of these

Options

A. a=2,b=-1
B. a=2,b=`-1//2`
C. a=-2,b=`1//2`
D. none of these

Answer

2

Explanation

We have `f(X) =a log|x|+bx^(2) +x`
or `f(X) =(a)/(x)+2bx+1`
since f(X) attains its extremum values at x=1,2
f(-1) =0 and f(X) =0
or -a-2b+1 and `(a)/(2)`+4b+1=0 or a =2 and b =-`1//2`