迭代的每一步的间隔宽度

Question

请告诉我，在Mathematica中是一个可以找到间隔宽度的标准函数吗？ 我必须为每次迭代找到它。

     (*Newton's method*)
 step[f_, iter_, inter_] := 
  Module[{x = Mean@First@(List @@ inter)//N}, 
   Print["Iteration ", iter, ".\n", "Interval is: ", inter, 
    "; \nx0_=", x, "; \nf(x0_)=", f[x], "; \nf'(interval)=", f'[inter],
     ";","\nIntervalsWidth=",(*??????????*),"\nX1=",IntervalIntersection[inter, x - (f[x])/(f'[inter])]]; IntervalIntersection[inter, x - (f[x])/(f'[inter])]]
newton[f_, inter0_, eps_] := 
  Module[{iter = 0},  
    N@Mean@First@(List @@ 
         NestWhile[(++iter; step[f, iter, #]) &, inter0, 
          Abs[Subtract @@ First@(List @@ #)] > eps &])];
f[x_] := x*x - 8*x + 7 ;
inter := Interval[{5, 17}] ;
newton[f, inter, 0.00001];

//////试图做

 (*Newton's method*)
 step[f_, iter_, {a_, b_}] := 
  Module[{inter = Interval[{a, b}],x =(a+b)/2}, 
   Print["Iteration ", iter, ".\n", "Interval is: ", inter,";\nIntervalsWidth=",b-a,
    "; \nx0_=", x, "; \nf(x0_)=", f[x], "; \nf'(interval)=", f'[inter],
     ";","\nX1=",IntervalIntersection[inter, x - (f[x])/(f'[inter])]]; IntervalIntersection[inter, x - (f[x])/(f'[inter])]]
newton[f_, {a_, b_}, eps_] := 
  Module[{iter = 0},  
    N@Mean@First@(List @@ 
         NestWhile[(++iter; step[f, iter, #]) &, {a,b}, 
          Abs[b-a] > eps &])];
f[x_] := x*x - 8*x + 7 ;
newton[f, {5, 17}, 0.00001];