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ISI2014-DCG-13

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Let the function $f(x)$ be defined as $f(x)=\mid x-1 \mid + \mid x-2 \:\mid$. Then which of the following statements is true?

  1. $f(x)$ is differentiable at $x=1$
  2. $f(x)$ is differentiable at $x=2$
  3. $f(x)$ is differentiable at $x=1$ but not at $x=2$
  4. none of the above
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Option D

The f(x) is neither differentiable at x=1 nor at x=2 because f(x) is pointed at both x=1 and x=2, though it is continuous in (-inf,+inf)

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