examday

/TMUA

In this question, $f(x)=ax^3+bx^2+cx+d$ and $g(x)=px^3+qx^2+rx+s$ are cubic polynomials.

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

• I $a>p$
• II if $b=q$ then $c=r$
• III $d>s$