ISI2014-DCG-13

Question

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?

• A. $f(x)$ is differentiable at $x=1$
• B. $f(x)$ is differentiable at $x=2$
• C. $f(x)$ is differentiable at $x=1$ but not at $x=2$
• D. none of the above

Answer 1

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)