Let $f \in C^2([a,b])$. How can I show that there has to exist a $C>0$ such that for all $x,y \in [a,b]$ we have $f'(x) - f'(y) \leq C(x-y)$ using Taylor-expansion (and the Lagrange-formula)?
2026-04-20 06:57:55.1776668275
Taylor: $f'(x) - f'(y) \leq C (x-y)$
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