Linear Approximation/Newton's Method
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Video Lecture 14 of 18
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### Lecture Description

The slope of a function y(x) is the slope of its tangent line. Close to x=a, the line with slope y ' (a) gives a "linear" approximation.

y(x) is close to y(a) + (x - a) times y ' (a)
If you want to solve y(x) = 0, choose x so that y(a) + (x - a) y ' (a) = 0
This is a really fast way to get close to the exact solution to y(x) = 0:
"Newton's Method" -- x = a - y(a)/y '(a)

### Course Description

Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject.

The series is divided into three sections:
Introduction
- Why Professor Strang created these videos
- How to use the materials

Highlights of Calculus
- Five videos reviewing the key topics and ideas of calculus
- Applications to real-life situations and problems
- Additional summary slides and practice problems

Derivatives
- Twelve videos focused on differential calculus
- More applications to real-life situations and problems
- Additional summary slides and practice problems

Acknowledgements
Special thanks to Professor J.C. Nave for his help and advice on the development and recording of this program.The video editing was funded by the Lord Foundation of Massachusetts.