Ask MetaFilter questions tagged with derivative

A nowhere continuous derivative?

thrako — Fri, 01 Aug 2008 19:23:47 -0800

Is there a differentiable function f(x) such that the derivative is nowhere continuous? That is, f'(x) has no point of continuity? Googling has led me to believe this does not exist, though I can't find anything like a proof, only vague references to Baire classes.

Can you tell me where I would find a proof?

Copyright issues in creating an ebook?

SampleSize — Fri, 28 Mar 2008 14:27:17 -0800

I'm thinking of creating an ebook that is a workbook companion for an existing popular investment book. What copyright issues do I have to consider? For example, can I title it "The [Investment Book Title] Workbook?" Can I do it at all without getting permission first?

Copyright in screenshots? Who owns it?

baylink — Tue, 23 Jan 2007 19:53:09 -0800

Can anyone explain, in some detail, precisely *how* the taking and use of a screenshot of a program running on a computer can infringe the copyrights or trademarks of others? There's a foofaraw going on just now on one of the Wikipedia mailing lists about the fact that Wikimedia Commons has what I, personally, feel is *entirely* too strict a policy concerning screenshots (where, by too strict, I mean that in the example of a screenshot of a website in a browser, they're concerned with infringing on the copyright not only of the website and it's designers and copywriters -- which I could just barely understand -- but also the trademark of the browser creator (for its logo) and the copyright of the creator of the desktop manager design -- Apple's Aqua, by example).

My assertion is that if I create a screenshot, *I* own a copyright in it, and that any infringement could only be by defining it as a derivative work. I thought I understood "derivative work", but they're trying really hard to convince me I'm out of my mind.

To be clear, they don't require that the program be a browser: they're just as happy to claim these infringements about screenshots of other types of running programs.

Certainly any of those party's lawers could convince them to sue, whether they have clear and reasonable grounds or not, and they have more money than you do -- though WMF certainly has a legal budget these days after a $1.5MUS pledge drive last month.

So, in the real world, can a screenshot -- given that screenshots are almost uniformly made either for identification, illustration, or educational purposes -- *actually* infringe any of those things?

(Extra points for case law; I'll be happy to look up the citations myself.)

I know we have some lawyers, I know this won't be legal advice, I also know it's federal jurisdiction, so the usual "I'm in another state" reply will matter less. Any thoughts?

Dumb calculus question...

killdevil — Wed, 19 Jul 2006 15:27:50 -0800

Stupid calculus question inside. So I have a detailed plot of a curve that looks rather like exponential decay, but no equation has been given to me to describe the curve.

I would like to find the instantaneous slope of the curve at any given point along its length. Am I correct in assuming that this is really just the first derivative? (I took calculus a long time ago).

I have been provided with a method for finding slope at any point along the curve by physically drawing a tangent to the point and computing ITS slope. Given my desire to use basic calculus to solve this instead, is there an easier/better way for me to calculate slope that doesn't involve irritating sketching of tangent lines and use of straight edges?

A concise, simple-to-grok explanation of what I need to do will win the day....