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Post Closed as "Not suitable for this site" by Andrés E. Caicedo, Alexandre Eremenko, coudy, David Handelman, Michael Renardy
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Ali
Ali
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This may be a trivial question but I can't see it immediately.

Suppose $\{a_k\}$ is an increasing sequence of positive reals. Does there exist a smooth function $f \in C^{\infty}([0,1])$ such that $\sup \partial^k f \ge a_k$$\inf \partial^k f \ge a_k$ holds for all $k$?

This may be a trivial question but I can't see it immediately.

Suppose $\{a_k\}$ is an increasing sequence of positive reals. Does there exist a smooth function $f \in C^{\infty}([0,1])$ such that $\sup \partial^k f \ge a_k$ holds for all $k$?

This may be a trivial question but I can't see it immediately.

Suppose $\{a_k\}$ is an increasing sequence of positive reals. Does there exist a smooth function $f \in C^{\infty}([0,1])$ such that $\inf \partial^k f \ge a_k$ holds for all $k$?

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Ali
Ali
  • 4.1k
  • 2
  • 13
  • 22

non-analytic functions with arbitrary large derivatives

This may be a trivial question but I can't see it immediately.

Suppose $\{a_k\}$ is an increasing sequence of positive reals. Does there exist a smooth function $f \in C^{\infty}([0,1])$ such that $\sup \partial^k f \ge a_k$ holds for all $k$?