**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.

**The Program **

'NEWTON' | {' is in ALPHA} {This is the name of the program} |

"INITIAL GUESS"?X | {" is in ALPHA} {? is in PRGM} { is on the , button} |

Lbl 1 | {Lbl is in PRGM under JMP} |

XA | |

X-Y1 Y2X | {Y1 is in VAR under GPH, then followed by a 1} |

X | { is in PRGM} |

X A Goto 1 | { , Goto are in PRGM under JMP} { is in PRGM under REL} |

**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
EXE 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