Question:
If \( f(x) = |x| + |x-1| \), then which of the following is correct?
- A. \( f(x) \) is both continuous and differentiable at \( x=0 \) and \( x=1 \)
- B. \( f(x) \) is differentiable but not continuous at \( x=0 \) and \( x=1 \)
- C. \( f(x) \) is continuous but not differentiable at \( x=0 \) and \( x=1 \)
- D. \( f(x) \) is neither continuous nor differentiable at \( x=0 \) and \( x=1 \)