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For a real number y, let [y] denotes the...

For a real number y, let [y] denotes the greatest integer less than or equal to y. Then the function `f(x) = fractan[(x-pi)pi] (1+[x]^2`is :

A

discontinuous at some x

B

continuous at all x, but the derivative f'(x) does not exist for some x

C

f'(x) exist for all x, but the derivative f''(x) does not exist for some x

D

f'' (x) exists for all x.

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The correct Answer is:
D
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