If `f(x)=alog|x|+b x^2+x` has extreme values at `x=-1` and at `x=2,` then find a and b .

Explanation

`f(x)=a log _{e}|x|+b x^{2}+x `


`f^{prime}(x)=a / x+2 b x+1`



`x=-1,2` are extreme of `f(x)`



`Rightarrow {f^{prime}(-1)=0={f}^{prime}(2) `


`Rightarrow-{a}-2 b+1=0 ldots ldots(1) text { and } {a} / 2+4 b+1=0 ldots`



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