examday

/TMUA

Which of the following statements about polynomials $f$ and $g$ is/are true?

• I. If $f(x)\ge g(x)$ for all $x\ge0$, then $\displaystyle\int_0^x f(t)\dd t\ge\int_0^x g(t)\dd t$ for all $x\ge0$.
• II. If $f(x)\ge g(x)$ for all $x\ge0$, then $f'(x)\ge g'(x)$ for all $x\ge0$.
• III. If $f'(x)\ge g'(x)$ for all $x\ge0$, then $f(x)\ge g(x)$ for all $x\ge0$.