Clear["Global`*"]
 (*Newton's Method for solving equation f(x)=0.,I do not understand \
 something like that you want to get?!,
 I'm nubie in Wolfram Mathematica - but experts don't answer you,
 See if code can help you with something. Excuse me for my broken \
 English*)
 
 (*function f(x)*)
 f[x_] := x - E^(-x^2);
(*Interval*)
interval = {0, 2};
(*desired accuracy*)
desAcc = 0.00001`;


(*Initial x - Mean of interval you chose*)
xInitial = Mean[interval];


(*Newton's Method*)
newton[f_, xInitial_, desAcc_] :=
Module[
  {xNext = 0, xNow = xInitial, result = desAcc, iter = 0},
  While[ result >= desAcc,
    iter++;
   
    xNext = N[xNow - (f[xNow]/f'[xNow])];
    result = Abs[xNext - xNow];
   
    If[ result < desAcc,
     Print[
      "Solve of equation f(x)=0 is for x = ",
      xNext, "."];
     Print["With accuracy ",
      desAcc, "."];
     Print["In interval ",
      interval, "."];
     Print["Loop counts: ",
      iter, "."],
     xNow = xNext
     ];
    ];
  ]

(*Newton's Method*)
newton[f, xInitial, desAcc];

Abs[f[p]] > eps &]

Abs[f[p]/f'[p]]> eps &]

Module[{p := Mean@First@(List @@ inter)},

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

NestWhile[(++iter; step[f, #]) &, inter0, Abs[f[p]] > eps &]