How to SolveWithout a Calculator?

[baha jaff]

hello Friends, I cant solve out this problem. For the following function, find a point of maxima and point of minima by hand ,if these exist
The function is f(x)=abs(x)+abs(x-2)

 

[tkhunny]

Where does each turn around?

Speaking from left to right

abs(x) decreases to x = 0, then increases

abs(x-2) decreases to x = 2, then increases

Together, then f(x) decreases quickly to x = 0, levels off between x = 0 and x = 2, then moves on up after x = 2.

You should think on these things BEFORE you turn on your calculator, anyway!