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+ \frac{f(x)}{x^2} \bigg] =$$3$, then $f(2) $ is equal to :

Question

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