Method of Differentiation
Differentiability of Absolute Value Functions
Premium Question
Grade 12
Question:
The function $f(x) = |x - 1| + |x + 1|$, $x \in \mathbb{R}$, is NOT differentiable at:
(1) exactly one point
(2) exactly two points
(3) exactly three points
(4) every point
Step-by-Step Solution
Key Concept: Split the real line into the intervals determined by the critical points $x = -1$ and $x = 1$, write $f$ as a piecewise linear function on each, and compare one-sided slopes at the junctions.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)