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If f(x)=alog|x|+b x^2+x has its extremum...

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

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
`y = a log x + b x ^(2) + x ` has extremum at ` x = - 1 and x = 2`.
`therefore " " ( dy )/(dx) = 0 ` at `x = -1`
and ` " "x = 2 rArr (a)/(x) + 2 bx + 1 = 0, at x = -1 `
and ` x = 2 `
`therefore " " - a - 2b + 1 = 0`
and ` " " (a)/(2) + 4b + 1 = 0`
`rArr " " a = 2 and b = - (1)/(2)`
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