The points at which the function $f(x)=|x-0.5|+|x-1|+\tan x$ does not have a derivative in the interval $(0,2)$ is

• A

  $0.5,1,2$
• B

  $0.5, \frac{\pi}{2}, 0$
• Correct answer
  C

  $1, \frac{\pi}{2}, 2$
• D

  $0.5,1, \frac{\pi}{2}$

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