If f (x) = 3a|2x - 4| - ax, where a is some constant, find f ′ (2).

|x| is x if x>0

|x| is - x if x<0

|x| is 0 if x=0

so

(|x|) '=1 when x>0

so

(|x|) '=-1 when x<0

(|2x-4|) '=2 when x>2

and

(|2x-4|) '=-2 when x<2

Therefore the left derivative doesn't equal the right derivative as x approaches 2.