\(A = | x + 2014 | + | x + 2015| + 2015\)
\(A = | x + 2014 | + | x + 2015 | + 2015 \)\(\ge\)
\(2015\)
\(Dấu " = " xảy \) \(ra\) \(\Leftrightarrow\)\(x + 2014 = 0 hoặc x + 2015= 0\)
\(\Leftrightarrow\)\(x = - 2014 hoặc x = - 2015\)
\(Min A = 2015\) \(\Leftrightarrow\)\(x = - 2014 hoặc x = - 2015\)
\(A=\left|x+2014\right|+\left|x+2015\right|+2015\)
\(=\left|x+2014\right|+\left|-x-2015\right|+2015\)
Ta có: \(\left|x+2014\right|+\left|-x-2015\right|\ge\left|x+2014-x-2015\right|=1\)
\(\Rightarrow\left|x+2014\right|+\left|-x-2015\right|+2015\ge2016\)
Dấu"="xảy ra \(\Leftrightarrow\left(x+2014\right)\left(-x-2015\right)\ge0\)
\(\Leftrightarrow\hept{\begin{cases}x+2014\ge0\\-x-2015\ge0\end{cases}}\)hoặc \(\hept{\begin{cases}x+2014< 0\\-x-2015< 0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x\ge-2014\\x\le-2015\end{cases}}\)hoặc \(\hept{\begin{cases}x< -2014\\x>-2015\end{cases}\left(loai\right)}\)
\(\Leftrightarrow-2014\le x\le-2015\)
Vậy \(A_{min}=2016\)\(\Leftrightarrow-2014\le x\le-2015\)
