A = |2x-x| + |2x-2013|
Ta có:
\(\left|2x-x\right|\ge0\forall x\)
\(\Rightarrow\)GTNN của |2x-x|=0
\(\left|2x-2013\right|\ge0\forall x\)
\(\Rightarrow\)GTNN của |2x-2013|=0
Dấu "=" xảy ra khi:
\(\left\{\begin{matrix}2x-x=0\Rightarrow x=0\left(1\right)\\2x-2013=0\Rightarrow2x=2013\Rightarrow x=\dfrac{2013}{2}\left(2\right)\end{matrix}\right.\)
\(\left(1\right)x=0\)
\(A=\left|2.0-0\right|+\left|2.0-2013\right|\\ A=0+\left|-2013\right|\\ A=0+2013\\ A=2013\)
\(\left(2\right)x=\dfrac{2013}{2}\)
\(A=\left|2.\dfrac{2013}{2}-\dfrac{2013}{2}\right|+\left|2.\dfrac{2013}{2}-2013\right|\\ A=\left|2013-\dfrac{2013}{2}\right|+\left|2013-2013\right|\\ A=\left|2013\right|+\left|0\right|\\ A=2013\)
Vậy \(Min_A=2013\) tại \(x=0\) hoặc \(x=\dfrac{2013}{2}\)