  We remark that there is no smooth function $f(x)$ on $[0, 1]$ which is flat
at $0$ such that the derivative $f^{(n)}$ of any order $n\geq 0$ is positive on
$(0,1]$. Moreover, the number of zeros of the $n$-th derivative $f^{(n)}$ grows
to the infinity and the zeros accumulate to $0$ when $n \to \infty$.
