The function `y=alogx+bx^2+x` has extreme values at x=1,2.Find a and b

Explanation

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

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

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

`Rightarrow a/1+2 b(1)+1=0`

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

`f^prime(2)=0`

`Rightarrow a/2+2 b(2)+1=0`

`Rightarrow a+8 b=-2`

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