#### Answer

x = 1

#### Work Step by Step

For absolute values, the derivative does not exist wherever the graph hits a minimum. This is where the sharp point occurs.
The minimum of an absolute value is 0, since an absolute value cannot be negative.
$ 0 = | x - 1 | $
Splits into $ 0 = x - 1 $ and $ 0 = - x + 1 $.
The solution for both of these equations is x = 1.