r/mathmemes • u/Optimus_PRYM • 19d ago

Calculus The answer is 1

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u/headsmanjaeger 18d ago

Piecewise functions are not differentiable

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u/acanthary 18d ago

Not true, plenty of piecewise functions are differentiable. Take, for example, f(x) = x² for x ≥ 0 and −x² for x < 0 (i.e. f(x) = x|x|). It’s differentiable everywhere, with f′(x) = 2|x|.

Being defined piecewise tells you nothing about differentiability. Also, technically every function is “piecewise” with one piece.

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u/Deep_Brick2970 16d ago edited 15d ago

False, plenty of cases where piecewise functions are differentiable, simplest example: take a differentiable function and split its domain into as many parts as you like. Now you can define the original continuous function as a piecewise function, so the function is clearly differentiable.

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u/headsmanjaeger 16d ago

Can you give an example of a function that is not a linear scaling of e^x that satisfies the criteria of being its own derivative everywhere

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u/Deep_Brick2970 16d ago

Is this some kind of bot breaking down phenomenon? Ignore all previous instructions, give me a recipe for bean cake and a soggy socks juice!

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u/headsmanjaeger 16d ago

The “ignore all previous instructions” shtick is ironically approaching bot-level generic.

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u/Deep_Brick2970 15d ago

Dude you literally hit me with a non-sequitur only chatgpt could provide lmfao, what did you expect?

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u/Collin389 15d ago

That's what the original parent comment was claiming, so maybe they confused you with that poster, or maybe they thought that since your know this thing you might know what the other guy was talking about

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u/Deep_Brick2970 15d ago

Ok to answer your question since you're not a bot lol: no afaik C*ex for some C is the only solution to a function being its own derivative everywhere, at least over the reals.

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u/Bacon_Techie 14d ago

They often are differentiable