Does eventually all the successive derivatives of a bounded functions become bounded if one of them becomes bounded?(for entire number line case)
2026-03-25 07:38:13.1774424293
Bounded function and Derivatives
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No, they don't. Consider $$ \sin(x^2) $$ which is clearly bounded, but whose derivatives all are very much unbounded.
However, if your function is defined on a closed and bounded interval, and all its derivatives exist everywhere (and are therefore all continuous), then they must be bounded.