The function f(x) = |x| + |x − 1| is continuous at x = 1 but not differentiable at x = 0 and x = 1. The number of points of non-differentiability of f(x) in [−1, 2] is:
The function f(x) = |x| + |x − 1| is continuous at x = 1 but not differentiable at x = 0 and x = 1. The number of points of non-differentiability of f(x) in [−1, 2] is:
- A. 0
- B. 1
- C. 2
- D. 3
Answer: C) 2
Explanation: f(x) = |x| + |x − 1| has sharp turns at x = 0 and x = 1 where derivative does not exist. In [−1, 2] both points lie, so 2 points of non-differentiability.
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