(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that if f(x) is Holder continuous, i.e,

[tex] \sup_{a<x , y<b} \frac{\abs{f(x) - f(y)}}{\abs{x-y}^\alpha} = K^f_\alpha<\inf [/tex]

with [tex] \alpha > 1 [/tex], then f(x) is a constant function

2. Relevant equations

3. The attempt at a solution

I've been staring at this for a while, but I'm unsure of where to start. I'm guessing that I'm supposed to show that the derivative of something is zero. I've seen hints elsewhere about applying Taylor's theorem, but I am unsure on how to apply it.

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# Homework Help: Holder Continuity question

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