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.
- Choose Intermediate Calculus from the initial menu and press
- Use the arrow keys to move to the menu item Newton-Raphson, press
- At the prompt F(x) =, enter the formula
x^3 - x^2 + 6x -8
- Enter the initial point at the prompt x_0 =
- Using the arrow keys, move to the item Graph Iterations and press
- We now enter the endpoints of the domain which we want to consider;
- a0 = 0
- a1 = 3
- 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
- At the prompt b = , type 30 .
- 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.