I've taken a calculus class for a semester at university as a mandatory part of my curriculum. In this class, we were taught formal definitions of what are derivatives and integrals, how to calculate them, and shown some of their generic applications (locating the local extrema of functions, finding the area of a shape enclosed between two curves etc.) However, despite finishing that course and passing the exam, I feel that I'm still missing the most important thing to know - when to use it. After the calculus class came a physics class, and whenever the lecturer told us that a problem is best solved by applying an integral, I simply took his word for it, being unable to understand why this was.
What I'm interested is not examples of common uses of calculus (I can easily find plenty with a simple web search). Rather, what I would like to know is how to tell if a solving a particular problem will require using calculus, when it isn't one of the commonplace scenarios that I brought up in the first paragraph. In the case of algebra, there are certain keywords that are helpful in figuring out what to do in a task (add, sum, increase imply addition; times, product imply multiplication, and so on). Are there similar keywords that hint that a task is to be solved by calculus? And if not, can this be deduced from the problem's description in other ways?
I am in awareness that after taking a calculus class and solving different tasks that are representative cases of their usage, I should be able to recognise other situations where it is necessary. Unfortunately, this simply went over my head, and now upon being told that a problem is best solved with calculus, I sit pondering how to come to such a conclusion, to no avail.