$y' = 0 \Leftrightarrow -3x^2 + 3m = 0 \Leftrightarrow \left[\begin{array}{l}x = - \sqrt m\\x = \sqrt m\end{array}\right.$
$\Rightarrow \left[\begin{array}{l}y = -(-\sqrt m)^3 + 3m.(-\sqrt m) + 1\\y = - (\sqrt m)^3 + 3m\sqrt m + 1\end{array}\right.$
$\Rightarrow \left[\begin{array}{l}y = -2m\sqrt m + 1\\y = 2m\sqrt m + 1\end{array}\right.$
$\Rightarrow A(-\sqrt m; -2m\sqrt m +1), B(\sqrt m; 2m\sqrt m + 1)$
$\Rightarrow \overrightarrow{OA} = (-\sqrt m; -2m\sqrt m +1);\, \overrightarrow{OB} = (\sqrt m; 2m\sqrt m + 1)$
$\Rightarrow \overrightarrow{OA}.\overrightarrow{OB} = (-\sqrt m).\sqrt m + (1 - 2m\sqrt m)(1 + 2m\sqrt m) = 1 - 4m^3 - m$
$ΔOAB$ vuông tại $O$
$\Leftrightarrow \overrightarrow{OA}.\overrightarrow{OB} = 0$
$\Leftrightarrow 4m^3 + m - 1 = 0$
$\Leftrightarrow m = \dfrac{1}{2}$
