1. Newton's Method
Lesson 3.8

2. Newton Views Roots
Consider a function as it crosses the x-axis (the root)
Newton saw that the tangent line close to the root crossed the x-axis close to the root
Try this on Geogebra

3. Newton's Method That line intersection can be easily calculatedx1 x2
That line intersection can be easily calculated
Let y = 0, solve for x
Use that point as a second (and usually better) estimate for the root of the function

4. Newton's Method for Approximating Roots
Given f(x) we seek a root
If xn is an approximation for the root
Then we claim is a better approximation •
xn+1 x1

5. Example Given Use to approximate the root
Continue the process until the approximations differ by less than .001
Use Calculator

6. Using the TI Calculator
Create a function called newt(n)
Assumes existence of f(x)

7. Newton's Failure
Remember that we said that usually we get a better estimate each time
Consider
Try it with your calculator

8. Newton's Method Spreadsheet
We will create a spreadsheet which demonstrates this concept

9. Assignment
Lesson 3.8
Page 195
Exercises 1 – 21 EOO, 29, 41