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$If y = a \log | x | + b x^{2} + x has its extremum values at x = - 1 and x = 2, then$

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a = 2, b = −1

a = 2, b = −1/2

a = −2, b = 1/2

none of these

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Correct option is B

We have y′=alx+2bx+1 and y′(−1)=0 and y′(2)=0∴ −a−2b+1=0 and a/2+4b+1=0⇒ a/2−2a+2+1=0 Hence a=2 and b=−1/2

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If y=alog⁡|x|+bx2+x has its extremum values at x=−1 and x=2, then

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$If y = a \log | x | + b x^{2} + x has its extremum values at x = - 1 and x = 2, then$