Let $\;f , g :R \to R\;$be two functions defined by $\;f(x)=\{ \begin{matrix}x sin(\large\frac{1}{x}) \;, x \neq 0 \\ 0\;,x=0 \end{matrix}\;$ , and $\;g(x)=x f(x)\;$\[\] Statement I : f is a continuous function at x=0 .\[\] Statement II : g is differential function at x=0 .