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