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!

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Local Extrema of Functions Exhibiting Self-Similarity

Loading...

Similar Threads - Local Extrema Functions | Date |
---|---|

Local max and min (including a domain) | Dec 4, 2015 |

Local uniform continuity of a^q | Aug 19, 2014 |

Second Derivative Test for Local Extrema | Apr 5, 2014 |

Local extrema | Feb 3, 2010 |

Finding the local extrema of this function | Jan 26, 2009 |

**Physics Forums - The Fusion of Science and Community**