Question

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

Answer 1

so would the answer be DNE?

Explanation:

Answer 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.