Programs for Newton's Method

The following programs will allow you to use a calculator to easily compute the successive approximate roots that Newton's Method provides. When you are prompted to "INPUT x" you should enter your initial guess at a root x0 and press "ENTER". The program will then display the values of f (x), f'(x), and the new and improved approximate root x1. Press "ENTER" repeatedly to produce x2, x3, x4, x5, etc. until you are satisfied that you have found a root. To exit the program, press "ON" and the appropriate button then presented to you. If you would like to then try another guess at a root, simply press "ENTER" again and the program will restart.

For the TI-81 and TI-82 calculators

Prgm: STEPNEWT
:Disp "INPUT X"
:Input X
:Lbl 1
:Disp "F(X)="
:Disp Y1
:Disp "DF(X)="
:Disp Y2
:X-Y1/Y2®X
:Disp "NEW X="
:Disp X
:Pause
:Goto 1
:End
:

To solve for the roots of the equation f (x)=0, you must enter the function f (x) as Y1 and calculate and enter its derivative f '(x) as Y2 under the "Y=" menu.

For the TI-85 calculator

Prgm: STEPNEWT
:Disp "Input x"
:Input x
:Lbl loop
:Disp "f (x)="
:Disp y1
:Disp "Df(x)="
:Disp y2
:x-y1/y2®x
:Disp "new x="
:Disp x
:Pause
:Goto loop
:End
:

To solve for the roots of the equation f (x)=0, you must enter the function f (x) as y1 and calculate and enter its derivative f'(x) as y2 under the "GRAPH" menu.