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Let [x] denote the greatest integer func...

Let `[x]` denote the greatest integer function and `f(x) =max {1+x+[x], 2+x, x +2[x]}, 0 le x le 2`. Let m be the number of points in `[0, 2]` , where f is not continuous and `n` be the number of points in `(0, 2)`, where `f` is not differentiable. Then `(m+ n)^2+2` is equal to

A

2

B

11

C

3

D

6

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