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

Alright
we consider 3 cases
1. where the absolute value is less than 0
2. where the absolute value is equal to 0
3. where the aboslute value is greater than 0

where is it equal to 0?
|2x-4|=0
2x-4=0
2x=4
x=2

at x=2 is the important point

so we have a piecewise function
f(x)=(-1)3a(2x-4)-ax for x<2
f(x)=-ax for x=2
f(x)=3a(2x-4)-ax for x>2

so take the dervitivive of each

f(x)=(-1)3a(2x-4)-ax for x<2
-7ax+12a
f'(x)=-7a for x<2

f(x)=-ax for x=2
f'(x)=-x for x=2
but wait, it changes derivitives at that opint so the dervitive ther is undefined

f(x)=3a(2x-4)-ax for x>2
f'(x)=5a for x>2

f'(2) is undefined