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NDA 2017 Maths · Mathematics · Continuity and Differentiability · easy

The number of points at which f(x)=|x-1|+|x-2| is not differentiable is

Single correct option

The number of points at which f(x)=∣x−1∣+∣x−2∣f(x)=|x-1|+|x-2| is not differentiable is
  1. A. 00
  2. B. 11
  3. C. 33
  4. D. 22
Show answer and solution

Answer: (D) 22

Each modulus term has a corner where its argument vanishes, at x=1x=1 and x=2x=2. At x=1x=1 the left slope is −2-2 and the right slope is 00; at x=2x=2 the slopes are 00 and 22. So there are exactly 22 points. The sum of two such terms does not smooth the corners.
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Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake