\(y'=3x^2-3=0\Rightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
\(\Rightarrow A\left(1;m-2\right)\) ; \(B\left(-1;m+2\right)\)
\(\Rightarrow\left\{{}\begin{matrix}OA=\sqrt{1+\left(m-2\right)^2}=\sqrt{1+\left(2-m\right)^2}\\OB=\sqrt{1+\left(m+2\right)^2}\\AB=2\sqrt{5}\end{matrix}\right.\)
\(T=OA+OB+AB=2\sqrt{5}+\sqrt{1+\left(2-m\right)^2}+\sqrt{1+\left(m+2\right)^2}\)
\(T\ge2\sqrt{5}+\sqrt{\left(1+1\right)^2+\left(2-m+m+2\right)^2}=4\sqrt{5}\)
Dấu "=" xảy ra khi \(2-m=m+2\Leftrightarrow m=0\)
