Not sure what kinda calculus you took at least here in the states it's very standard to learn about such functions in class, and yes there is a difference between discontinuous and the slope being really large (though finite) for a brief period of time

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ajkjk 4 hours ago | parent | next [-]

You rarely study delta and step functions in an introductory calculus class. In this case the first derivative would be a step function, in the sense that over any finite interval it appears to be discontinuous. Since you can only sample a function in reality there's no distinguishing the discontinuous version from its smooth approximation.

(I suppose a rudimentary version of this is taught in intro calc. It's been a long time so I don't really remember.)

	▲	Neywiny 3 hours ago \| parent [-]
		I'm sure it depends on who's teaching the class and what curriculum they follow, but we were doing piecewise linear functions well before differentiation so I think I do actually disagree as per your caveat. It's also possible that the courses triaged different material. As a calc for engineers not calc for math majors taker, my experience may have been heavier on deltas and steps.

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alwa 3 hours ago | parent | prev [-]

Not to be all “do you know who X is,” but I did have to chuckle a little when I saw who it is that you’re teaching differentiation to here…