1. 3.8 Newton’s Method
How do you find a root of the following function without a graphing calculator?
This is what Newton did.

2. Let’s begin with this:
Example 1: Calculate the first three approximations x1, x2, x3 to a root of f(x) = x2 – 5 using the initial guess x0 = 2. (means approximating )

3. Example 2: Calculate 3 iterations of Newton’s Method to approximate zero.

4. Example 3: Show that the following function has
four real roots with
x0 = 0, Newton’s Method converges to the root near -2.
x0 = -1, Newton’s Method converges to the root near -1.