Continuity and differentiability of x^n sin(1/x) at x = 0

1. A.
   $f$ is continuous but not differentiable
2. B.
   $f$ and $f'$ both are continuous
3. C.
   $f'$ is continuous but not differentiable
4. D.
   $f$ is continuous but $f'$ is not continuous

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1. A.
   $f^{''}(0) = 1$
2. B.
   $f^{''}\left( \frac{2}{\pi} \right) = \frac{24 - \pi^{2}}{2\pi}$
3. C.
   $f^{''}\left( \frac{2}{\pi} \right) = \frac{12 - \pi^{2}}{2\pi}$
4. D.
   $f^{''}(0) = 0$

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