Discuss the continuity and differentiability of the function `f(x)=|x|+|x-1|` in the interval (-1, 2).

Explanation

To discuss the continuity and differentiability of the function \( f(x) = |x| + |x - 1| \) in the interval \((-1, 2)\), we will analyze the function step by step.

### Step 1: Identify the critical points
The absolute value function can change its behavior at certain points. For \( f(x) = |x| + |x - 1| \), we need to find the points where the expressions inside the absolute values are zero:
1. \( |x| = 0 \) at \( x = 0 \)
2. \( |x - 1| = 0 \) at \( x = 1 \)

Thus, the critical points are \( x = 0 \) and \( x = 1 \).
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