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 MPP:

  1. At the main menu, either enter 2 or use the arrow keys to move to 2. Root and press
  2. At the prompt for method, type in n and,
  3. at the prompt for function, type x^3 - x^2 + 6x - 8
  4. At the prompt for the derivative type: 3x^2 - 2x + 6
  5. We now enter the endpoints of the domain which we want to consider; enter
    Xmin = 0
    Xmax = 3
    and press
  6. At the prompt Number of digits accuracy , type 6 .
  7. Press to draw the graph.
  8. At this point, you will see the graph and you will be prompted to enter the "guess" to use; type 2.9 .
  9. You will now see the program draw the tangent line and pick the point. This process continues until the point is too close to the root to visualize and the program then rescales the coordinates.

  10. Press to return to the screen at which you entered the endpoints of the first subinterval. You could try to find another root of the function at this time.