If f(x) = abs(x - 1) + 1, then f'(1) = ?

Question

Would the answer be 0 or nonexistent. f'(1) = 0/0, so would this be considered nonexistent?

Answer 1

if y = |x-1| + 1
graph it
x and y
0 2
1 1
2 2
straight lines each side of (1,1) with different slopes.
Thus the derivative is discontinuous (changes from -1 to +1) at x = 1 and is undefined at that point.