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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 = xnf(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.