F1[x_] = x (x+1)

F2[x_] = (x^2)(x+1)

NewtF1[x_] = x-F1[x]/D[F1[x],x]

NewtF2[x_] = x-F2[x]/D[F2[x],x]

(N[NestList[NewtF1[#]&, SetPrecision[100,20],20],12])//MatrixForm

(N[NestList[NewtF2[#]&, SetPrecision[100,20],40],12])//MatrixForm

F5[x_] = (x^5)(x+1)

NewtF5[x_] = x-F5[x]/D[F5[x],x]

(N[NestList[NewtF5[#]&, SetPrecision[100,20],40],12])//MatrixForm

Q2[x_] = (x^2)+2

NewtQ2[x_] = x-Q2[x]/D[Q2[x],x]

(N[NestList[NewtQ2[#]&, SetPrecision[1,50],30],20])//MatrixForm

(N[NestList[NewtQ2[#]&, SetPrecision[I,50],30],20])//MatrixForm

(N[NestList[NewtQ2[#]&, SetPrecision[-10 I,50],30],20])//MatrixForm

NewtF[x_] = x-(((x^2)-2x)/(2x-2))

Simplify[NewtF[x]]

SNewtF[x_] = Simplify[((D[NewtF[x],{x,3}])/(D[NewtF[x],x]))-(3/2)(((((D[NewtF[x],{x,2}])/(D[NewtF[x],x]))))^2)]

DNewtF[x_] = Simplify[D[NewtF[x],x]]

Plot[DNewtF[x],{x,-3,3},PlotRange->{{0,2},{-1,1}}]

(N[NestList[NewtF[#]&, SetPrecision[0.75,50],10],20])//MatrixForm

(N[NestList[NewtF[#]&, SetPrecision[1.25,50],10],20])//MatrixForm

Plot[{x,NewtF[x]},{x,-2,4}, PlotRange->{{-2,4},{-5,5}}]

(N[NestList[NewtF[#]&, SetPrecision[(1/2),50],10],20])//MatrixForm

(N[NestList[NewtF[#]&, SetPrecision[0.1,50],10],20])//MatrixForm

Plot[{x,NewtF[x]},{x,-2,0.5}, PlotRange->{{-2,0.5},{-1,1}}]

FNew[x_] = (1/x)-1

NewNewtF[x_] = Simplify[x-((FNew[x])/(D[FNew[x],x]))]

(N[NestList[NewNewtF[#]&, SetPrecision[-2,50],10],20])//MatrixForm

(N[NestList[NewNewtF[#]&, SetPrecision[0.1,50],10],20])//MatrixForm

(N[NestList[NewNewtF[#]&, SetPrecision[5,50],10],20])//MatrixForm

(N[NestList[NewNewtF[#]&, SetPrecision[2,50],10],20])//MatrixForm

(N[NestList[NewNewtF[#]&, SetPrecision[1.9,50],10],20])//MatrixForm

D[NewNewtF[x],x]

D[NewNewtF[x],x]/.x->1

Simplify[((D[NewNewtF[x],{x,3}])/(D[NewNewtF[x],x]))-(3/2)(((((D[NewNewtF[x],{x,2}])/(D[NewNewtF[x],x]))))^2)]

(N[NestList[NewNewtF[#]&, SetPrecision[2.01,50],10],20])//MatrixForm