Newton Rhapson

[guiltfeeder]

Hi there
I was wondering if anyone could explain how to show the Newton Rhapson method on autograph, drawing all the tangents on the graph.
Thanks for the support,
Ryan

[Douglas]

> ... how to show the Newton Raphson method on Autograph, drawing all the tangents on the graph

There are three methods in fact

1. Manually: place a point on the graph and select it; draw a tangent, select the tangent, use "solve f(x)=0" to find where it cuts the x-axis. Put a point on this intersection, then a vertical line through the point, and you have completed one cycle.  

If you are on v.3, you can use CTRL in the Point Mode to find the intersection of the tangent with the x-axis in one step.

2. Select the graph. Use right-cliick "Newton-Raphson Iteration", enter the start value of \'x\', then click the buttons to see the iterations.

3. Place a point on the graph, and select it. Use the right-click option "Newton-Raphson Iteration", and click the buttons to see the iterations. The advantage of method 3 is you can now move the point along the graph.

Hope this helps.