# Construct function out of extrema, roots...

Is there a way in sage to construct and plot a smooth function which has a given set of data:

- the minima $(miA_1,miA_2)$, $(miB_1,miB_2)$,...
- the maxima $(maA_1,maA_2)$, $(maB_1,maB_2)$,...
- the roots $(nA1,nA2)$, $(nA1,nA2)$...
- a given behaviour for $x \to \pm \infty$.

I don't think so (this would be a strange feature to have), but you can do it analytically through calculus and other methods. Do you need help doing that?

If you have a good idea how to do it, it would be nice if you could explain it.