Output data on iterations correctly

Questions
1

PLEASE help to edit this code to output data on each iteration because it outputs only on the last…
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PLEASE help to edit this code to output data on each iteration because it outputs only on the last…

[b]step[f_,inter_] := Module[{x=Mean@First@(List @@ inter)}, [/b]

[b]    IntervalIntersection[inter, x - (f[x])/(f'[inter])]] [/b]

[b] newton[f_, inter0_, eps_] := Module[{iter = 0}, [/b]

[b]    Print["X1 = ", N@Mean@First@(List @@ [/b]

[b]    NestWhile[(++iter; step[f, #]) &, inter0, [/b]

[b]        Abs[Subtract @@ First@(List @@ #)] > eps & ])]; [/b]

[b]        Print["iter=", iter]; [/b]

[b]        Print["Iteration ",iter,".\n","Interval is: ",inter,"; \nx0_=", [/b]

[b]            x= Mean@First@(List @@ inter) ,"; \nf(x0_)=",f[x],"; \nf'(interval)=",f'[inter],";"]]; [/b]

[b]f[x_] := x*x - 8*x + 7; [/b]

[b]inter := Interval[{1,9}]; [/b]

[b]newton[f, inter, 0.00001];[/b]
2

To print something at each step, try making the Print statements part of the step function.

step[f_, iter_, inter_] := 
 Module[{x = Mean@First@(List @@ inter)}, 
  Print["Iteration ", iter, ".\n", "Interval is: ", inter, 
   "; \nx0_=", x, "; \nf(x0_)=", f[x], "; \nf'(interval)=", f'[inter],
    ";"]; IntervalIntersection[inter, x - (f[x])/(f'[inter])]]

newton[f_, inter0_, eps_] := 
 Module[{iter = 0}, 
  Print["X1 = ", 
    N@Mean@First@(List @@ 
         NestWhile[(++iter; step[f, iter, #]) &, inter0, 
          Abs[Subtract @@ First@(List @@ #)] > eps &])];]
3

Thank You veeery much!

please, Could You help me to write this Newton’s method not in interval but in the mean of Interval??? and in ‘While’ it could be while the function(point)>eps So I only has to change

p := Mean[{5, 9}]; f'[p] ; f'[inter]; n0 = p - f[p]/f'[p]; 

x1 = IntervalIntersection[p,n0];

I tried to write it
but again iterations doesn’t work correctly;(

step[f_,inter_] := Module[{p:=Mean@First@(List @@ inter)},

IntervalIntersection[inter, p - (f[p])/(f'[p])]]

newton[f_, inter0_, eps_] := Module[{iter = 0},

Print["X1 = ", N@Mean@First@(List @@

NestWhile[(++iter; step[f, #]) &, inter0, 

    Abs[f[p]] > eps & ])];

    Print["iter=", iter];

    Print[ "loop counts: ", iter, ". ", inter,"; p=",p=Mean@First@(List @@ inter), "; f[p]=",f[p],"; f'[p]=",f'[p]]];

f[x_] := x*x - 8*x + 7;

inter := Interval[{5,9}];

newton[f, inter, 0.00001];