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Question

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

A
a=34,b=18
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B
a=34,b=18
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C
a=34,b=18
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D
None of these
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Solution

The correct option is A a=34,b=18
Around x=1,3 we have |x|=x
f(x)=aloge|x|+bx2+x
f(x)=ax+2bx+1
From the question, f(1)=0,f(3)=0
a+2b+1=0,a3+6b+1=0
Solving we get a=34 and b=18

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