\[\begin{array}{l} y = \frac{1}{3}{x^3} + \left( {m - 2} \right){x^2} + \left( {m - 2} \right)x + 3m + 1\\ \Rightarrow y' = {x^2} + 2\left( {m - 2} \right)x + m - 2 = 0\\ co\,\,\Delta ' = {\left( {m - 2} \right)^2} - m + 2 = \left( {m - 2} \right)\left( {m - 3} \right).\\ TH1:\,\,HS\,\,\,DB\,\,tren\,\,\,R\\ \Rightarrow \Delta ' \le 0\\ \Leftrightarrow \left( {m - 2} \right)\left( {m - 3} \right) \le 0\\ \Leftrightarrow 2 \le m \le 3.\\ TH2:\,\,y' = 0\,\,co\,\,2\,\,nghiem\,\,pb\,\,{x_1};\,\,{x_2}\\ \Rightarrow \Delta ' > 0\\ \Leftrightarrow \left( {m - 2} \right)\left( {m - 3} \right) > 0\\ \Leftrightarrow \left[ \begin{array}{l} m > 3\\ m 2\\ \left( {{x_1} - 1} \right)\left( {{x_2} - 1} \right) \ge 0 \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} {x_1} + {x_2} > 2\\ {x_1}{x_2} - \left( {{x_1} + {x_2}} \right) + 1 \ge 0 \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} - 2\left( {m - 2} \right) > 2\\ m - 2 + 2\left( {m - 2} \right) + 1 \ge 0 \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} m - 2

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