**Introduction**

This program finds successive approximations to the solutions of
*f*(*x*) = 0
using Newton's method.

If you have not used one of the programs posted on this website before,
you should read through
the information in the Intro to Programming section first.

If you have a TI Connectivity Cable, you can download the program main.newt.89p

**The Program**

:newt( ) | {This will already appear if you named the program newt} |

:Prgm | {This will already appear} |

:ClrIO | {ClrIO is in the CATALOG menu} |

:Input "initial guess", x | {Input is in the F3 menu} { x is the x button} |

:0 c | { is the STO button} {0 is a zero} |

:Lbl p | {Lbl is in the CATALOG menu} |

:c+1c | |

:x-y1(x) / (d(y1(x),x))b |
{y1 is the Y button followed by a 1} {d is in the CATALOG menu} |

:Disp "step number", c | {Disp is in the F3 menu} |

:Disp "estimate is", b | |

:Pause | {Pause is in the CATALOG menu} |

:ClrIO | |

:b x | |

:Goto p | {Goto is in the CATALOG menu} |

:EndPrgm | {This will already appear} |

**Running the program**

You will need to enter *f*(*x*)into y1. After
entering an initial guess for the solution to *f*(*x*) = 0
, hit
ENTER to obtain each new approximation.
To test the program try the following:

*f*(*x*) = x^{3}-3x^{2}+x-5,
initial guess = 3.

The approximations should be

3.2

3.18019169329

3.17998109582

3.17998107216