Chapter 3 - Differentiation - 3.2 The Derivative as a Function - Exercises - Page 116: 71

x = 1

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.