Which of the following statements is true for the general cubic function $f\left(x\right)=a{x}^3+b{x}^2+cx+d$, $\left(a\ne 0\right)$.

$\mathrm{I}$. If the derivative $f^{\text{'}}\left(x\right)$ has two distinct real roots, then cubic has one local maxima and one local minima.

$\mathrm{II}$. If the derivative $f^{\text{'}}\left(x\right)$ has exactly one real root, then the cubic has exactly one relative extrema.

$\mathrm{III}$. If the derivative $f^{\text{'}}\left(x\right)$ has no real roots, then the cubic has no relative extrema