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

with the initial point **x = 3**.

Using Microcalc:

- Choose
*Intermediate Calculus*from the initial menu and press . - Use the arrow keys to move to the menu item
*Newton-Raphson*, press and . - At the prompt
*F(x) =*, enter the formulax^3 - x^2 + 6x -8 - Enter the initial point at the prompt
*x_0 =*2.9 . - Using the arrow keys, move to the item
*Graph Iterations*and press and - We now enter the endpoints of the domain which we want to consider;
enter
- 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 drawn.
- 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.