Question

The number of values of x ∈ [0,2]  at which f(x) = |x-1/2|+|x-1|+Tan x     is not differentiable at 
A) 0                                B) 1                      C) 2                   D) 3
Given the answer is option  D   please explain me how 

Answer 1

|x-1/2| is not differentiable at x-1/2 =0
=> x = 1/2
|x-1| is not differentiable at x-1 = 0
=> x = 1
Tanx is not differentiable at pi/2       (Tanx is not differentiable where its value is ∞ or -∞)
hence in [0,2] f(x)is not differentiable at three points