# NEWTON'S METHOD - TI 89 or TI 92

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) = x3-3x2+x-5, initial guess = 3.

The approximations should be
3.2
3.18019169329
3.17998109582
3.17998107216