\[\begin{array}{l}
y = m{x^3} - {x^2} + 2{m^2}x + 2m - 3\\
\Rightarrow y' = 3m{x^2} - 2x + 2{m^2}\\
\Rightarrow y' = 0\\
\Leftrightarrow 3m{x^2} - 2x + 2{m^2} = 0\,\,\left( * \right)\\
TH1:\,\,Hs\,\,luon\,\,co\,\,\,cuc\,\,tri \Leftrightarrow \left( * \right)\,\,\,co\,\,2\,\,nghiem\,\,phan\,\,biet\\
\Leftrightarrow \left\{ \begin{array}{l}
a \ne 0\\
\Delta ' > 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
m \ne 0\\
1 - 6{m^3} > 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m \ne 0\\
{m^3} < \frac{1}{6}
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
m \ne 0\\
m < \frac{1}{{\sqrt[3]{6}}}
\end{array} \right..\\
TH2:\,\,m = 0\\
\Rightarrow y = - {x^2} - 3\,\,\,la\,\,\,ham\,\,so\,\,bac\,\,\,hai\,\,co\,\,1\,\,cuc\,\,\,tri.\\
Vay\,\,m < \frac{1}{{\sqrt[3]{6}}}\,\,\,thoa\,\,\,man\,\,bai\,\,toan.\,
\end{array}\]
