Sensitivity of a draggable point

Hello everyone,

Below is a copy of a screen I want to include with an activity. It works exactly as intended except at the minimums and maximums of the function and the x-intercepts. It seems the issue is that it seems challenging to drag the point to be EXACTLY at an intercept or at a minimum/maximum. Do you know of a way to fix this? Thank you in advance.

My first idea is to build in tolerance so that the x-coordinate (or slope) don’t have to equal exactly 0 but rather are within 0.05ish to get the message that they are actually 0. I don’t know of a way to actually fix the problem.

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Thank you for responding. Another workaround I found is to have a function where intercepts and extrema occur at precise values, rather than decimals you have to get right to the nearest hundredth. That works much better but still not ideal. I will ponder how to introduce the tolerance you mentioned. I’ll update the slide above if I am able to fix it. Thank you again.

This is a totally different look, but maybe something like this will work for you? It uses the cursor location to “trace” the function. With this, you can get creative with locking the point to certain locations just by comparing distances. Right now, this is only set up to pause at the x-intercepts, but other locations could be included. One downfall is the labels are only displayed as decimals, but I think you could use CL as a workaround to fix this. I didn’t go that far because I’m not sure if you would like this method. This might not work well on a mobile device either. Tracing a Function using currentX • Activity Builder by Desmos

What I had in mind was changing the test in your note to be something like

when bvalue>0.1 "positive"
when bvalue<-0.1 "negative"
otherwise "neither positive nor negative"

when dvalue>0.1 "increasing"
when dvalue<-0.1 "decreasing"
otherwise "neither increasing nor decreasing"
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I agree with @sergeballif, shifting the logic to the note and providing some breathing room that way is more flexible.

Would also suggest not hardcoding the derivative function and just calling it from the graph component itself.

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Your solution proved eminently workable, though I moved the characterization of the function from a text box to the graph itself. I am attaching the finished, fully functional screen. I could not have done this without you. Still mulling some of the ways in which the graphing calculator can be made to do things. I really appreciate your help.

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Thank you for your suggestion. It will be extremely useful to me in the future. You’ve given me several ideas that will enhance the functionality of my graphs. I appreciate it.