Q107 / 160 · TS EAMCET 2021 (06 Aug Shift 1) · Mathematics

If $f: R \rightarrow R$ is defined as $f(x)=|x+1|+|x-1|$, then $f(x)$ is

  • A
    not differentiable at every real number
  • Correct answer
    B
    not differentiable at - 1and 1 only
  • C
    not differentiable at - 1, 0 and 1
  • D
    differentiable on R

Solution

Given, $f(x)=|x+1|+|x-1|$ $f(x)$ has a corner point only at $x=1,-1$ by the graph. So, $f(x)$ is not differentiable at $x=-1,1$ only.

Hence, the correct answer is option: 'B'.

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