$\begin{array}{l}
y = f\left( {{x^2} - 2x} \right)\\
\Rightarrow y' = \left( {2x - 2} \right)f'\left( {{x^2} - 2x} \right)\\
\Rightarrow y' = 0 \Leftrightarrow \left[ \begin{array}{l}
2x - 2 = 0\\
f'\left( {{x^2} - 2x} \right) = 0
\end{array} \right.\\
Dua\,\,vao\,\,\,BBT\,\,cua\,\,dths\,\,y = f'\left( x \right)\,\,\,ta\,\,co:\\
f'\left( {{x^2} - 2x} \right) = 0 \Leftrightarrow \left[ \begin{array}{l}
{x^2} - 2x = {x_1}\,\,\,\left( {{x_1} < - 1} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\\
{x^2} - 2x = {x_2}\,\,\,\left( { - 1 < {x_2} < 0} \right)\,\,\,\,\,\,\,\,\,\,\,\left( 2 \right)\\
{x^2} - 2x = {x_3}\,\,\,\,\,\left( {0 < {x_3} < 1} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 3 \right)\\
{x^2} - 2x = {x_4}\,\,\,\,\,\left( {{x_4} > 1} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 4 \right)
\end{array} \right.\\
Xet\,\,pt\,\,\,{x^2} - 2x = {x_1} \Leftrightarrow {x^2} - 2x - {x_1} = 0\\
\Rightarrow pt\,co\,\,\,2\,\,\,nghiem\,\,\,pb \Leftrightarrow \Delta ' > 0 \Leftrightarrow 1 + {x_1} > 0 \Leftrightarrow {x_1} > - 1\,\,\,\,\left( {vo\,\,\,ly} \right)\\
\Rightarrow pt\,\,\left( 1 \right)\,\,\,\,VN\\
Tuong\,\,tu\,\,\,xet\,\,voi\,\,{x_2},\,\,\,{x_3},\,\,{x_4}\,\,\,ta\,\,\,thay\,\,cac\,\,pt\,\,\,\left( 2 \right),\,\,\left( 3 \right),\,\,\left( 4 \right)\,\,\,co\,\,2\,\,nghiem\,\,\,pb\,\,\, \ne 1\\
\Rightarrow hs\,\,\,co\,\,7\,\,\,diem\,\,cuc\,\,tri.
\end{array}$
