  In this short note we prove that, if (C[a,b],{A_n}) is an approximation
scheme and (A_n) satisfies de La Vall\'ee-Poussin Theorem, there are instances
of continuous functions on [a,b], real analytic on (a,b], which are poorly
approximable by the elements of the approximation scheme (A_n). This
illustrates the thesis that the smoothness conditions guaranteeing that a
function is well approximable must be, at least in these cases, global. The
failure of smoothness at endpoints may result in an arbitrarily slow rate of
approximation. A result of this kind, which is highly nonconstructive, based on
different arguments, and applicable to different approximation schemes, was
recently proved by Almira and Oikhberg (see arXiv:1009.5535v2).
