While studying the concept of maxima and minima, I came across a question:
The function $f(x)=2|x| + |x+2| - \left| |x+2| - 2|x| \right|$ Then at which points does the given function has a local minimum or a local maximum
Other than using software can this type of question be solved by plotting graphs of these functions??
Perhaps this will help:
$$\min\{a,b\} ={a+b-|a-b|\over 2}$$
so in your case $$f(x) =2\min\{|2x|,|x+2|\}$$
If $4x^2\geq (x+2)^2$ or $x\in (-\infty,-{2\over 3})\cup (2,\infty)$ we have $$f(x) = 4|x|$$ and for $x\in (-{2\over 3},2)$ we have $$f(x)=2|x+2|$$