format long
fpi(@(x) x-(1+x.^5-3*x-2*x.^3)/(5*x.^4-3-6*x.^2), 0.0, 0.000000001, 20)

ans =

                  0   0.33333333333333
   0.33333333333333   0.31392694063927
   0.31392694063927   0.31375560390870
   0.31375560390870   0.31375559086394
   0.31375559086394   0.31375559086394
   0.31375559086394   0.31375559086394

fpi(@(x) x-(1+x.^5-3*x-2*x.^3)/(5*x.^4-3-6*x.^2), +10, 0.000000001, 20)

ans =

  10.00000000000000   8.01666093082576
   8.01666093082576   6.43457013036314
   6.43457013036314   5.17500916819970
   5.17500916819970   4.17574078729860
   4.17574078729860   3.38821508993022
   3.38821508993022   2.77572434807706
   2.77572434807706   2.31255185551781
   2.31255185551781   1.98389013525226
   1.98389013525226   1.78396937995683
   1.78396937995683   1.70122800937365
   1.70122800937365   1.68733462434025
   1.68733462434025   1.68696969917752
   1.68696969917752   1.68696945196341
   1.68696945196341   1.68696945196329
   1.68696945196329   1.68696945196329

fpi(@(x) x-(1+x.^5-3*x-2*x.^3)/(5*x.^4-3-6*x.^2), -10, 0.000000001, 20)

ans =

 -10.00000000000000  -8.01670141911452
  -8.01670141911452  -6.43470110301740
  -6.43470110301740  -5.17535365474763
  -5.17535365474763  -4.17659757593184
  -4.17659757593184  -3.39030137876715
  -3.39030137876715  -2.78072700688811
  -2.78072700688811  -2.32425833583764
  -2.32425833583764  -2.00983549276571
  -2.00983549276571  -1.83452501283894
  -1.83452501283894  -1.77689864752601
  -1.77689864752601  -1.77107375475125
  -1.77107375475125  -1.77101764447360
  -1.77101764447360  -1.77101763930573
  -1.77101763930573  -1.77101763930573
  -1.77101763930573  -1.77101763930573

exit