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Question

If f(x)=a loge |x|+bx2+x has extremum at x = 1 and x = 3, then


A

a = -3/4, b= -1/8

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B

a=3/4, b= -1/8

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C

a =-3/4, b=1/8

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D

None of these

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Solution

The correct option is A

a = -3/4, b= -1/8


For x>0 or x<0f(x)=ax+2bx+1f(1)=0a+2b+1=0and f(3)=0a3+6b+1=0
Solving Eqs. (i) and (ii), we get
a = - 3/4, b = -1/8


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