Consider the following statements about the polynomial $\text{p}(x)$, where $a<b$:

I $\text{p}(a)\le \text{p}(b)$

II ${\text{p}}^{\prime }(a)\le {\text{p}}^{\prime }(b)$

III ${\text{p}}^{\prime \prime }(a)\le {\text{p}}^{\prime \prime }(b)$

Which of these statements is a necessary condition for $\text{p}(x)$ to be increasing for $a\le x\le b$?