Let x=-1 and x=2 be the critical points of the function f(x)=x^3+a x^2+b log_e |x|+1, x ≠ 0. Let m and M respectively be the absolute minimum and the…

Let $\displaystyle x=-1$ and $\displaystyle x=2$ be the critical points of the function $\displaystyle f(x)=x^3+a x^2+b \log _{\mathrm{e}}|x|+1, x \neq 0$. Let $\displaystyle m$ and M respectively be the absolute minimum and the absolute maximum values of $\displaystyle f$ in the interval $\displaystyle \left[-2,-\frac{1}{2}\right]$. Then $\displaystyle |\mathrm{M}+m|$ is equal to (Take $\displaystyle \log _{\mathrm{e}} 2=0.7$ ) :