## A function whose Nth derivative is nowhere differentiable. [closed]

Problem:

1. Given a natural number N, construct a function $f$:R->R which is a member of CN (the N times differentiable functions) for which the Nth derivative of $f$ is the Weirstrauss Function.

2. Find a differential equation satisfied by the solution of 1.

Alternatively, show that 1 and/or 2 is not possible.

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This looks very like homework for me. For (1) have you tried integrating the series for the Weierstrass function term-by-term? – Robin Chapman Aug 23 2010 at 17:17
Not homework, I just thought it was interesting because I am thinking a lot about these types of topics. See some of my other recent posts. – Matt Calhoun Aug 23 2010 at 17:21
The Weierstrass function (note spelling) $g$ is continuous, so by basic calculus it has antiderivatives of all orders. For (2), trivially there's $f^{(N)}=g$. Matt, based on your history I think unfortunately MO is not the right place for the types of questions you have. Please read the FAQ for other suggestions. And on any site, evidence that the question is not homework and that you have given it serious thought is worth including. – Nate Eldredge Aug 23 2010 at 17:27
ok sry! I wont post again. – Matt Calhoun Aug 23 2010 at 17:31