Consider $\mathrm{f}\left(\mathrm{x}\right)=\frac{\left({\mathrm{x}}^2-1\right)\left({\mathrm{x}}^2-4\right)}{\mathrm{g}\left(\mathrm{x}\right)}, \mathrm{x}\in \mathrm{R}-\left\{\mathrm{a},\mathrm{b}\right\},$ where g(x) is a polynomial of degree $\le 4$.

f(x) has a removable type of discontinuity at x = a and x = b. Also it is known that

$\begin{array}{l}\left(\mathrm{i}\right) \underset{\mathrm{x}\to \pm \infty }{\lim } \mathrm{f}\left(\mathrm{x}\right)=+\infty \\ \left(\mathrm{ii}\right) \underset{\mathrm{x}\to -1}{\lim } \mathrm{f}\left(\mathrm{x}\right)=6\\ \left(\mathrm{iii}\right) \underset{\mathrm{x}\to -2}{\lim } \mathrm{f}\left(\mathrm{x}\right)=\mathrm{a} \mathrm{non}-\mathrm{zero} \mathrm{finite} \mathrm{number}\end{array}$

Let L and, M denote the number of points of discontinuity and the number of points of non-derivatively respectively of any function in R. (R is the set of real numbers)