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min{x - [x], 1 + [x] - x} on an interval: points where it is not continuous or not differentiable

This type of question, asked 2 times: 2021 Paper 16, 2021 Paper 19. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 16

    55
    f(x)=f(x) = minimum {x−[x], 1+[x]−x}\{ x - \lbrack x\rbrack,\ 1 + \lbrack x\rbrack - x\}, [0,3]→R\lbrack 0,3\rbrack \rightarrow R, pp is the number of points where it is discontinuous, qq is the number of points where it is not differentiable. Find p+qp+q.

  2. Question 2

    2021 Paper 19

    61
    Let [t]\lbrack t\rbrack denote the greatest integer less than or equal to t. Let f(x)=x−[x],g(x)=1−x+[x]f(x) = x - \lbrack x\rbrack, g(x) = 1 - x + \lbrack x\rbrack, and h(x)=min⁡{f(x),g(x)},x∈[−2,2]h(x) = \min\{ f(x), g(x)\}, x\in \lbrack - 2, 2\rbrack. Then hh is:

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