Let f(x) be a polynomial of degree $4$ having extreme values at $x = 1$ and $x = 2.$ If $\mathop {lim}\limits_{x \to 0} \left( {{{f\left( x \right)} \over {{x^2}}} + 1} \right) = 3$ then f($-$1) is equal to :

Question

Let f(x) be a polynomial of degree $4$ having extreme values at $x = 1$ and $x = 2.$

If $\mathop {lim}\limits_{x \to 0} \left( {{{f\left( x \right)} \over {{x^2}}} + 1} \right) = 3$ then f($-$1) is equal to :

${9 \over 2}$