HOW TO USE NEWTON'S METHOD TO ESTIMATE THE ROOT OF A FUNCTION WITH TI89 CALCULATOR

Steps	Key Sequence	Screens
1. Input Function or Piecewise-Defined Function into Y1.	Press DIAMOND key, then F1 key (for Y=)
	Type the function
2. Input Derivative Function into Y2.	Press CATALOG, then the comma key
	Press ENTER
	Type y1(x)
	Press comma, then the independent variable, x
	Press ')', then ENTER
3. Go to Home screen	Press 2nd, then ESC
Note: The formula for Newton's Method is xn + 1 = xn – f(xn)/f ′(xn) where f(x) is y1(x) and f ′(x) is y2(x).
4. Store initial approximation, x0 into the variable x	Input number
	Press STO key, then X, then ENTER
5. Calculate the next approximation, x1, and store into the variable x	Type: x-y1(x)/y2(x), then STO, then X, then ENTER
6. Calculate the next approximation, x2, and store into the variable x	Press ENTER
7. Repeat Step 6, as necessary
Note: In this case, the root of the function is x = –1.2419.