Lời giải:Ta có \(f'\left( x \right) = m{x^2} - mx + 3 - m\).
\(\begin{array}{l}f'\left( x \right) > 0\,\,\forall x \in \mathbb{R} \Leftrightarrow \left[ \begin{array}{l}\left\{ \begin{array}{l}m = 0\\f'\left( x \right) = 3 > 0\,\,\forall x \in \mathbb{R}\end{array} \right.\\\left\{ \begin{array}{l}m \ne 0\\1 > 0\,\,\left( {luon\,\,dung} \right)\\\Delta = {m^2} - 4m\left( {3 - m} \right) < 0\end{array} \right.\end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l}m = 0\\5{m^2} - 12m < 0\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}m = 0\\0 < m < \dfrac{{12}}{5}\end{array} \right. \Leftrightarrow 0 \le m < \dfrac{{12}}{5}\end{array}\).
Chọn C.
