THE FEUTEX TOOLKIT

Newton Root-Finding Step

Perform one Newton root-finding iteration using a supplied function value and derivative.

Math workspace● Runs in your browser

01 Your input

Current estimatenumberFunction valuenumberDerivativenumber

02 Your result

View or copy raw result data

Result data

FormulaNext = x-fx/dfx; Step = -fx/dfx

Sources and model references

https://mathworld.wolfram.com/Newton-RaphsonMethod.html

Worked example

Inputs

Current estimate: 3 number
Function value: 5 number
Derivative: 6 number

Expected results

Next: 2.166666667 number
Step: -0.8333333333 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

Enter the labeled inputs using consistent units.
Check the stated assumptions and calculate.
Review each output and compare another input scenario.

Try this example

{
  "x": 3,
  "fx": 5,
  "dfx": 6
}

Accuracy and scope

One local iteration from supplied evaluations; convergence is not guaranteed. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.