Is the atlas containing only the chart (R, cube root) for a manifold (R, standard) a C^infinity? why? Let A={(R,cube root)} be an atlas for a manifold(R, standard topology).There is only one chart and no other in the atlas. Is the atlas C^infinity compatible? and why so?

The differentiable class of a Differentiable Manyfold is referenced a change parameters funcions. In this case, has "only" change parameters, in fact, the identity function over $\mathbb{R}$. Clearly, this function is $C^\infty$.