Re: Liptschitz function approximation

In article
<1165155034.578710.75470@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Li Yi" <liyi.cn@xxxxxxxxx> wrote:

Let f be a Liptschitz function on [0,1].
Show that there exists f_n in C^1([0,1]) and M such that
(i) |f_n'| <= M
(ii) lim f_n(x) = f(x), for all x in [0,1].

In fact there are polynomials that do the above; what class is
this, and what material are you covering at the moment?
.