Give a graphical demonstration of Newton's method to find the root of the equation

f(x) = x3 - x2 + 6 x - 8

with the initial point x = 3.

Using Microcalc:

  1. Choose Intermediate Calculus from the initial menu and press .
  2. Use the arrow keys to move to the menu item Newton-Raphson, press and .
  3. At the prompt F(x) =, enter the formula
    x^3 - x^2 + 6x -8
  4. Enter the initial point at the prompt x_0 =
    2.9 .
  5. Using the arrow keys, move to the item Graph Iterations and press and
  6. We now enter the endpoints of the domain which we want to consider; enter
    a0 = 0
    a1 = 3
  7. Now the computer prompts us for the range; it is important to enter an upper bound for the range; otherwise, the graphs of the lines will not be drawn.
  8. At the prompt b = , type 30 .
  9. Press several times; each press represents one iteration of Newton's method. Note that at the bottom of the screen is the current value for x_n.