Just for fun: Cubic Graph Plot

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    Cubic Fun Graph Plot
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SUMMARY

The discussion centers on using Desmos.com, an online graphing utility, to experiment with the Newton-Raphson method for solving cubic graphs. The method is applied to find x-intercepts, with users advised to increase iterations for improved accuracy. Two specific Desmos calculators are shared: one for cubic graphs and another for determining square roots using the function f(x)=x²-a. The latter includes a side panel displaying a more precise numeric value of the root.

PREREQUISITES
  • Understanding of the Newton-Raphson method
  • Familiarity with cubic functions and their properties
  • Basic knowledge of graphing utilities, specifically Desmos
  • Concept of x-intercepts in polynomial functions
NEXT STEPS
  • Explore advanced features of Desmos for graphing complex functions
  • Learn about iterative methods for root-finding in numerical analysis
  • Investigate the accuracy of Newton-Raphson compared to other root-finding algorithms
  • Study the implications of parameter selection in iterative methods
USEFUL FOR

Mathematicians, educators, students, and anyone interested in numerical methods and graphing techniques using Desmos for visualizing mathematical concepts.

neilparker62
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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
 
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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
 
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