## Description

- Overview:
- A visual demo of Newton's Method for pre-calculus students.

- Subject:
- Calculus, Geometry
- Level:
- Middle School, High School, Community College / Lower Division
- Material Type:
- Simulation
- Provider:
- GeoGebra
- Provider Set:
- GeoGebraTube
- Date Added:
- 04/26/2012

- License:
- Creative Commons Attribution Share Alike
- Language:
- English
- Technical requirements:
- Java
- Media Format:
- Interactive

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An outstanding visualization! You can enhance your visualization by adding the following algebraic explanation to your comment section:

Suppose the point you choose is [c, f(c)].

In order to find the second guess, we need the equation of the tangent line at x=c, after which, we can find where it intersects the x-axis to obtain the second guess.

So, let t(x)=f'(c) x + k where t(x) is the equation of the tangent line.

We determine k as follows:

f(c) = f'(c) c + k

=> k=f(c) - f'(c) c

=> t(x)=f'(c) x + f(c) - f'(c) c

=> t(x)=f'(c) [x - c] + f(c)

We know the tangent line intersects the x-axis when t(x)=0.

So,

0= f'(c) [x - c] + f(c)

=> x - c = - f(c) / f'(c)

=> x = c - f(c) / f'(c)

This last equation provides the next guess, that is, x as expected.

John Gabriel

http://thenewcalculus.weebly.com.

http://whatyouhadtoknowbutyoureducators.weebly.com/the-new-calculus-course.html