Consider $[\cdot]$ and ${\cdot}$ denote the greatest integer function and the fractional part function, respectively.
Let $f (x) = {x} + \sqrt{{x}}$ .
Statement I: f is not differentiable at integral values of x.
Statement II : f is not continuous at integral points

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Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I

Both Statement I and Statement II are correct but Statement II is not the correct explanation of Statement I

Statement I is correct but Statement II is incorrect

Statement II is correct but Statement I is incorrect

answer is A.

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The function is not differentiable and continuous at two points between $x = - π / 2$ and $x = π / 2$ . Also, the function is not continuous at $x = \frac{π}{2}$ and $x = - \frac{π}{2}$ . Hence, at four points, the function is not differentiable.