$$\eqalign{ & 34)\,\,y = {m \over 3}{x^3} - \left( {m - 1} \right){x^2} + 3\left( {m - 2} \right)x + {1 \over 3}\,\,\,DB/\left( {2; + \infty } \right) \cr & y' = m{x^2} - 2\left( {m - 1} \right)x + 3\left( {m - 2} \right) \cr & TH1:\,\,m = 0 \Rightarrow y' = 2x - 6 > 0 \Leftrightarrow x > 3 \cr & \Rightarrow HS\,\,DB/\left( {3; + \infty } \right) \Rightarrow Loai \cr & TH2:\,\,m \ne 0 \cr & \Delta ' = {\left( {m - 1} \right)^2} - 3m\left( {m - 2} \right) = - 2{m^2} + 4m + 1 \cr & + \,\,Ham\,\,so\,\,DB/R \Rightarrow y' \ge 0\,\,\forall x \in R \cr & \Rightarrow \left\{ \matrix{ m > 0 \hfill \cr \Delta ' = {\left( {m - 1} \right)^2} - 3m\left( {m - 2} \right) \le 0 \hfill \cr} \right. \cr & \Leftrightarrow \left\{ \matrix{ m > 0 \hfill \cr - 2{m^2} + 4m + 1 \le 0 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{ m > 0 \hfill \cr \left[ \matrix{ m \ge {{2 + \sqrt 6 } \over 2} \hfill \cr m \le {{2 - \sqrt 6 } \over 2} \hfill \cr} \right. \hfill \cr} \right. \Leftrightarrow m \ge {{2 + \sqrt 6 } \over 2} \cr & + \,\,\Delta ' > 0 \Rightarrow {{2 - \sqrt 6 } \over 2} 0 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{ {x_1} + {x_2} 0 \hfill \cr} \right. \cr & \Leftrightarrow \left\{ \matrix{ {{2\left( {m - 1} \right)} \over m} 0 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{ 2\left( {m - 1} \right) 0 \hfill \cr} \right. \cr & \Leftrightarrow \left\{ \matrix{ 2m - 2 0 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{ 2m > - 2 \hfill \cr 3m - 2 \ge 0 \hfill \cr m > 0 \hfill \cr} \right. \cr & \Leftrightarrow \left\{ \matrix{ m > - 1 \hfill \cr m \ge {2 \over 3} \hfill \cr m > 0 \hfill \cr} \right. \Leftrightarrow m \ge {2 \over 3} \cr & Ket\,\,hop\,\,cac\,\,TH\,\,ta\,\,co\,\,m \ge {2 \over 3} \cr & Chon\,\,A. \cr} $$