Question

If $y=a\log \left|x\right|+b{x}^2+x$ has its extremum values at $x=-1$ and $x=2$ then the value of $-2ab$ is

Answer 1

If $y=a\log \left|x\right|+b{x}^2+x$ has its extremum values at $x=-1$ and $x=2$
$\frac{dy}{dx}=\frac{a}{x}+2bx+1$
As $y=a\log \left|x\right|+b{x}^2+x$ has extremum at $x=-1$ and $x=2$
$-a-2b+1=0$
$\frac{a}{2}+4b+1=0$
On solving both equations, we get
$a=2$ and $b=-1/2$
Now, we have to calculate $-2ab$
$=-2\times 2\times \frac{-1}{2}$
$=2$