The question primarily asks to sketch, draw, or analyse the graph of a function built from absolute value expressions, including piecewise representations.
The function $f ( x ) = 2 | x | + | x + 2 | - | | x + 2 | - 2 | x | |$ has a local minimum or a local maximum at $x =$ (A) $- 2$ (B) $\frac { - 2 } { 3 }$ (C) $2$ (D) $\frac { 2 } { 3 }$