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$If f (x) = a \log_{e} | x | + b x^{2} + x has extremums at x = 1 and x = 3, then$

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a=−34,b=−18

a=34,b=−18

a=−34,b=18

a=12,b=−1

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detailed solution

Correct option is A

at x=1,3 we have |x|=x∴f(x)=aloge⁡x+bx2+x∴f′(x)=ax+2bx+1 According to question, f′(1)=0,f′(3)=0∴a+2b+1=0,a3+6b+1=0 On solving, we get a=−34,b=−18

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

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Ready to Test Your Skills?

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$If f (x) = a \log_{e} | x | + b x^{2} + x has extremums at x = 1 and x = 3, then$