Newton’s Method TI-85

Open the graphing screen. | |

^{3} as y1 | |

^{2} as y2 | |

Return to the home screen. | |

This is a new program. | |

NEWTON | Use the letters in blue at the upper right of the keys to type the program name. |

Press the key until the pointer is pointing at y1. | |

Press the key until the pointer is pointing at y2. |

Formula is x - y1/y2; store the result in x | |

Display x. | |

Quit programming. |

- Enter the function x
^{2}- 4x as y1 in your grapher. - Enter the derivative 2x - 4 as y2; return to the home screen
- Store the initial guess of 3 in X:
- Run the program: ; the resulting value is the first approximation for the zero.
- For each successive iteration, press again. If two successive values are the same, that is the best approximation for the zero that the program will find.