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

Given : `f(x)=y=a log x+b x^{2}+x`



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



Since, `f^{prime}(x)` has extreme values at `{x}=1` and `{x}=2, f^{prime}(1)=0`.



`Rightarrow frac{a}{1}+2 b(1)+1=0 `


`Rightarrow a=-1-2 b ldots(1) `


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