Hi guys. Today was my last day of Calculus I class, and I’ve had this question simmering in my mind for some time now. Perhaps you guys may enlighten me or point me in the right direction?(adsbygoogle = window.adsbygoogle || []).push({});

Consider the Weierstrass function, which is continuous everywhere but differentiable nowhere. We know that a local extremum, let’s say a local maximum, means that there is a number b, a < b < c, such that f(b) >= f(x) in (a, c). We also know that a local extremum either has a derivative of 0 or is non-differentiable.

My question is: Is it possible for every point of the Weierstrass function to be a local extremum (considering it is a non-constant function), given its self-similarity? If you look at it from one viewing rectangle it appears as if it the function has a maximum/minimum at a point in a given neighborhood, but then you zoom in and zoom in and zoom in. . . .

If not, how does one locate the points in which there is a local extremum?

Sorry if that was a lame question, and thanks in advance!

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# Local Extrema of Functions Exhibiting Self-Similarity

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