MATH151
Newton’s Method TI-85

1. To enter the Newton’s method program in your calculator:
Open the graphing screen.
Enter the function 7x -x3 as y1 
Enter the derivative 7 - 3x2 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.
2. To run the program for f(x) = x2 - 4x with derivative f ´(x) = 2x - 4 and initial guess xo = 3:
  1. Enter the function x2 - 4x as y1 in your grapher.
  2. Enter the derivative 2x - 4 as y2; return to the home screen
  3. Store the initial guess of 3 in X:  
  4. Run the program: ; the resulting value is the first approximation for the zero.
  5. 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.