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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
by ajkjk 11mo ago
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 11mo agoI'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.