Calculus (3rd Edition)

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.