1. NEWTON’S METHOD
Section 3.8

2. When you are done with your homework, you should be able to…
Approximate a zero of a function using Newton’s Method

3. Appollonius lived in 250BC. He studied conic sections
Appollonius lived in 250BC. He studied conic sections. Name the three conic sections and how Appollonius characterized the ellipse.
The three conic sections are the circle, ellipse and hyperbola. Appollonius characterized the ellipse as the perpendicular of a flat plane with a cone.
The three conic sections are the circle, ellipse and hyperbola. Appollonius characterized the ellipse as the perpendicular of a flat plane that is parallel to the side of a cone.
The three conic sections are the parabola, ellipse and hyperbola. Appollonius characterized the ellipse as the perpendicular of a flat plane that is parallel to the side of a cone.
The three conic sections are the parabola, ellipse and hyperbola. Appollonius characterized the ellipse as the perpendicular of a flat plane with a cone.

4. NEWTON’S METHOD
Newton’s Method uses tangent lines to approximate zeros
The assumption is that the function and the tangent line cross the x-axis at about the same point

5. NEWTON’S METHOD FOR APPROXIMATING THE ZEROS OF A FUNCTION
Let where f is differentiable on an open interval containing c. Then, to approximate c, use the following steps.
Make an initial estimate that is close to c. (Make a graph!)
Determine a new approximation
If is within the desired accuracy, let serve as the final approximation. Otherwise, return to step 2 and calculate a new approximation.
*Each successive application of this procedure is called an iteration.

6. Use Newton’s Method to approximate to five decimal places.