NewtonsMethodList[f_,{x_,x0_},n_]:=NestList[#-Function[x,f][#]/Derivative[1][Function[x,f]][#]&,x0,n]

f[x_]=((x^3)+12 x-3.1)/25; 
g[x_] = x - f[x]/((3x^2+12)/25);
h[x_]=x;
t1[x_]=f[2]+f'[2](x-2);
h1[x_]=g[2];
Plot[{f[x],g[x],h[x],t1[x],h1[x]},{x,0,2},PlotStyle->Magenta] (Print["y = f[x] = ",f[x]];)

NewtonsMethodList[f[x],{x,2},10]

SecantMethodList[f_,{x_,x0_,x1_},n_]:=NestList[Last[#]-{0,(Function[x,f][Last[#]]*Subtract@@#)/Subtract@@Function[x,f]/@#}&,{x0,x1},n]

SecantMethodList[f[x],{x,2, 0.7958333333333334},10]