Writing a loop for multiple derivatives along with roots for each derivative

Question

I am trying to write a loop that will take the first n derivatives (lets say n =3), which outputs a list that will include 1(or more) roots for each derivative. I haven't actually set up the loop because I'm not quite sure which I want to use. (Do, For, While, maybe even Table) Here is what I have so far and I know I will need to use each of these somewhere in my loop.

 Clear[x,roots,x,n];
 f[x_] = x^8 - 3 x^5 + x - 1;

 NSolve[f'[x] == 0, x, Reals];

 Table[D[f[x], {x, n}], {n, 1, 3}]

I'm just not sure how I should start honestly.. I've been having difficulties with loops in Mathematica. Even a simple suggestion as to which loop I should use would be great (I know you could solve this using any of the loops but I'm not that familiar with them yet).

Any help/advice is always appreciated!

Brandon

* I GOT IT!*

 Clear[x, roots, x, n, d];
 f[x_] = x^8 - 3 x^5 + x - 1;
 n = 5;
 der = D[f[x], {x, #}] & /@ Range[n];
 roots = Table[NSolve[der[[#]] == 0, x, Reals] & /@ Range[n]];
 Grid[{der, roots} // Transpose]

Thanks to all.

Answer 1

You don't really need a loop at all. Here is the function and it's n derivatives:

f[x_] := x^8 - 3 x^5 + x - 1;
n=3;
der = D[f[x], {x, #}] & /@ Range[n]

Then map NSolve to all the answers:

NSolve[der[[#]] == 0, x] & /@ Range[n]