alt Hacker NewsNot 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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alwa • yesterday at 6:58 PM
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…
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.)