If $f(x)$ is continuous and differentiable function and $f(1/n)=0\forall n \geq 1$ and $n\in 1$ then

Question

$\begin{array}{1 1}(a)\;f(x)=0\;x\in (0,1)\\(b)\;f(0)=0,f'(0)=0\\(c)\;f(0)=0=f'(0)\;x\in(0,1)\\(d)\;f(0)=0\;and\;f'(0)\;need\;not\;be\;zero\end{array}$