Which polynomial will give the minimum value on given x.

Question

We are given n polynomials $p_1(x), p_2(x), \dotsc, p_n(x)$. Each polynomials is of the form $p(x) = ax^3+bx^2+cx+d$, where $a$, $b$, $c$, and $d$ are whole numbers up to $10^5$. We are given $x_0$. And we have to find $p_i(x)$ such that $p_i(x)$ has minimum value among all $n$ polynomials.