In this question, $\text{f}(x)=a{x}^3+b{x}^2+cx+d$ and $\text{g}(x)=p{x}^3+q{x}^2+rx+s$ are cubic polynomials.

If $\text{f}(x)-\text{g}(x)>0$ for every real $x$, which of the following is/are necessarily true?

I $a>p$

II if $b=q$ then $c=r$

III $d>s$