Here is an interesting situation.
I have noticed that when using evaluateAt and attempt to evaluate the derivative of e^x something is not working. The first screen evaluates a trig function, but see what happens in the second screen. Testing derivative of e^x
I first found this situation in this awesome activity by Christopher Sewards @Christophe_Sew. I looked and looked but was unable to find the reason, so I created a small activity (above) to test, and I am finding the same issue.
(Product Rule • Activity Builder by Desmos)
I am wondering if it has to do with e being irrational or something like that.
You can see that the second check fails, and you’re right, it’s down to some small error Desmos introduces in its calculations. Here I’ve check the input evaluated at x=3 and the graph version of that same calculation. Not quite the same.
I don’t recommend evaluateAt for this sort of thing. Use a statistical total and allow for some error bound.
Also, the way this question is set up introduces a lot of brittle code. Try to use something more abstracted that works in many situations. It’ll make doing these sorts of things much more template-y and keep it DRY.
Here’s something I use quite often. It does the following:
abstracts the function latex to the note itself
imports that function into the graph, so that you never need touch the graph ever again - just change the note and everything still works
calculates the total number correct for the student
persistently shows a check mark on the dashboard if the student gets one - or more - correct.
Thank you Mike, I appreciate your feedback. I have notice similar errors now in other compound functions. There is still a lot I have to learn in desmos, but situations like this allow me to move a bit further each time.
Saludos,
here is my activity (modified from Alfonso’s and piggybacked off of some of Mike Gleason’s suggestions.)
The problem gets typed into the top of the table, and that’s it. (“Template-y”)
It works well for most functions. (Not e^x and ln x)
I was going to just go with “round”, to see how that works. (Addendum: worked like a charm for e^x - but “ln” is still wonky)
I also added a check number usage example that works well with quotient rule problems. The code would require an edit each time to check for numbers in the simplified answer.
I added a few slides. I used the rounding for any derivatives involving e^x, and it works.
But it still is a bit strange on the last slide with ln x. Any ideas on why it does not work for some of the variations, I would much appreciate it.
I tried to enter some functions that might cause trouble. A lot of them just require clear use of parentheses so there is no “ambiguity”
ex: sin x cos x is not accepted, but (sinx)(cosx) and sin(x)cos(x) is fine.
Isn’t the last slide just ambiguity issues as well? Neither ln x cos x nor cos x ln x work, but putting brackets around either the initial x or the initial function seem to work just fine:
This was a question from an old AP exam. The correct multiple choice is exactly the way this is typed in, and it is saying no…but if I put the parentheses around the 3x in the two trig functions, it says Yay. I guess my point is, is the AP answer not correctly given? I guess the route to go is to tell students to put the argument of the function in parentheses when in doubt. Probably not a bad habit.
If anyone is still on this thread, here is my template that can be used to crank out a bunch of “find the derivative” problems.
If anyone has any edits/suggestions/improvements, let me know.
sorry, try as I may, I can’t get rid of the kid in the box. That gif is not anywhere in the activity anymore, and I keep deleting it from the activity home page. That might need a new thread “How to permanently delete the image that displays”
