I was trying to construct some functions, but I don´t know how I can do it Dx. The first it´s a continuous function, that has exactly the set $$ \left\{ 0 \right\} \cup \left\{ {\frac{1} {n}} \right\} $$ as local strictly maximum points. My problem is with the point 0. Dx
The second is construct ( if it exist ) an infinite differentiable function, such that $$ \eqalign{ & f^{\left( k \right)} \left( 0 \right) = 1\,\,\forall k \in {\Bbb N} \cr & f\left( 0 \right) = 1 \cr} $$ and it´s different from the exponential.
here it´s obvious that if exist such function exist, and it´s different from the exponencial, could not be analytic, otherwise, i´ll be the exponencial, but I don´t have some example If someone can help me with that )=