Trying to derive this but has multiple absolute values

[souldoutt]

Homework Statement

Find the Local and absolute extrema of f(x) on the interval [-1,2] and give a sketch of the graph if:

f(x) = [ 1 / (1 + |x|) ] + [ 1 / (1 + |x - 1|) ]




I am confused about the absolute value parts. I know they're the versions inside the absolute value signs when >0 and the negative of the inside when < 0 but I'm not sure how to start this derivative.

Help would be appreciated. Thanks.

 

[Hurkyl]

I know they're the versions inside the absolute value signs when >0 and the negative of the inside when < 0

If you can't study both cases together, then study each case separately.