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If f(x)=alog|x|+b x^2+x has extreme valu...

If `f(x)=alog|x|+b x^2+x` has extreme values at `x=-1 a n d a t x=2,` then find a and b .

A

a=2 , b=-1

B

`a=2,b=-1//2`

C

`a=-2,b=1//2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have
`f(x) = alog|x|+bx^2+x rArr f'(x)a/x+2bx+1`
Since f(x) attains its extremum values at x=-1,2
`therefore f'(-1)=0 " and " f'(2) =0`
`rArr -a-2b+1=0 "and " a/2+4b+1=0`
`rArr a=2 "and " b=-1//2`
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