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If x = -1 and x = 2 are extreme points o...

If x = -1 and x = 2 are extreme points of f(x) = `alpha log|x| + beta x^2 + x`, then

A

`alpha =-6,beta=1/3`

B

`alpha =-6,beta=-1/2`

C

`alpha =2,beta=-1/2`

D

`alpha = 2,beta=1/2`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(X)=(alpha)/(x)+2betax+1`
`rarr 2betax^(2)+x+alpha`=0 has roots -1 and 2
`rarr alpha=2,beta =-1/2`
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