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If f(x)=sin(2pi[pi^2x])/(5+[x^2]) denote...

If `f(x)=sin(2pi[pi^2x])/(5+[x^2])` denotes the greatest integer function), then f(x) is

A

discontinuous at some x

B

continuous at all x, but the derivative `f'(x)` doesn't exist for some x

C

`f'(x) exists for all x, but `f''(x)` doesn't for some x

D

`f''(x) exists for all x.

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The correct Answer is:
D
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