Incremental search for root brackets
Claude prompt
This page was generated by Claude Code from the following prompt (with additional prompting):
Make an incremental search demo for f(x) = e^x − 4√x on [0, 2] that indicates the final root intervals and candidate intervals on a plot. Add a slider for the number of candidate intervals. Give a dropdown to select from two functions; the other one should have roots that are relatively easy to miss (Chapra has an example). Also add a toggle to turn on/off plotting of the actual function, so we have an option to see just "what the computer sees".
Incremental search splits the search range \([x_\text{min}, x_\text{max}]\) into \(n\) candidate intervals of width \(\Delta x = (x_\text{max} - x_\text{min})/n\) and evaluates \(f\) at every boundary. A candidate \([x_l, x_u]\) is kept as a root bracket when \(f(x_l)\,f(x_u) < 0\), because a continuous function that changes sign must cross zero somewhere in between.