Let $f(x) $ be a polynomial of degree four having extreme values at $x=1$ and $ x=2$ If $\lim\limits_{x \to 0} \bigg[1+\large\frac{f(x)}{x^2}\bigg]$$=3$ then $(2)$ is equal to :

Question

$\begin{array}{1 1} 0 \\ 4 \\ -8 \\ -4 \end{array} $