**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 NEWT.86p

**The Program**

:Disp "INITIAL GUESS" | {Disp and " are in PRGM under I/O} |

:Input x | {Input is in PRGM under I/O} {x is the x-VAR } |

:Lbl P | {Lbl is in PRGM under CTL} |

:xA | {The arrow is STO} |

:x-y1/y2x | {y1 and y2 are in CATLG-VARS under EQU} |

:Disp x | |

:Pause | {Pause is in PRGM under CTL} |

:If x A | {If is in PRGM under CTL} { is in TEST } |

:Goto P | {Goto is in PRGM under CTL} |

**Running the program**

You will need to enter *f*(*x*) and *f '*(*x*)
into y1 and y2, respectively. 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,
*f '*(*x*) = 3x^{2}-6x+1,
initial guess = 3.

The approximations should be

3.2

3.18019169329

3.17998109582

3.17998107216