I am working on a project where I have to group/classify calculus problems. Now with most the calculus topics, it's usually obvious how it's divided in various textbooks, but when it comes to related rates, all the textbooks I checked don't divide it further.

I was thinking of classifying the problems depending on whether it's "related time rate problem", "related rate problem", and on the geometrical shape/rule involved in the problem.

But I was wondering if there is a more standardized classification, a classification based on a textbook or if you have better suggestions than the ones I mentioned.

  • $\begingroup$ When I taught this, I tended to divide them into two types. For one of the types, after you differentiate both sides of some general equation (given explicitly or obtained from geometrical or other considerations), you just plug in everything you're given (e.g. values for $x,$ $y,$ $dx/dt,$ etc.) and only one unknown remains (what the problem asks for), and you solve for that unknown. The other type is when you don't have values for all but one of the unknowns, so you have to go back to given information and somehow (e.g. Pythagorean theorem) find the one or more additional values needed. $\endgroup$ Jun 19, 2017 at 15:08
  • $\begingroup$ Can you clarify the distinction? Isn't rate, by definition, something happening over time? What are you trying to accomplish by categorizing further? $\endgroup$ Jun 27, 2017 at 12:16


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