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

Question

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

MARKS App · Accepted Answer

d y d x = a x + 2 b x + 1 or d y d x = 0 at x = - 1 , 2 a - 1 + 2 b - 1 + 1 = 0 or - a - 2 b + 1 = 0 a 2 + 4 b + 1 = 0 or a + 8 b + 2 = 0 solving we get ; a = 2 , b = - 1 2

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