Newton's Method Lesson 3.8.

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Presentation transcript:

Newton's Method Lesson 3.8

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

Newton's Method That line intersection can be easily calculated x1 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

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

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

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

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

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

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