Just for fun: Cubic Graph Plot

[neilparker62]

TL;DR

Cubic Graph plot on Desmos

Desmos.com is a great online graphing utility which I'm sure is familiar to many PF users. I wanted to experiment with the Newton-Raphson method using it so chose solution of cubic graphs as an example. The graph shows a variable cubic on which all turning points and intercepts are calculated and shown. x-intercepts by Newton-Raphson.

I'm sure readers will find parameter values where the x-intercepts are not that accurate - in that case add a couple more "g(g(.." iterations!

https://www.desmos.com/calculator/lejtdd8fws

 

[neilparker62]

Here's another use of Newton-Raphson whereby the square root of a number is determined by finding the positive x-intercept of $f(x)=x^2-a$. The intercept is marked on the graph but the side panel shows a more accurate numeric value of the root against parameter d where $d=\sqrt{a}$. The start value for determination of the square root is the square root of the nearest square greater than a.

https://www.desmos.com/calculator/qbyev8tuqz