Assuming $f$ is single/double/triple/etc... differentiable, we know that if $f$ is increasing, then it has a positive first derivative and if $f$ is convex then it has a positive second derivative. What are the analogous characteristics of $f$ that guarantee it has a positive third/fourth/etc... derivative?
2026-05-14 19:02:53.1778785373
Sufficient conditions for a continuous function to have a positive (negative) third derivative? Fourth derivative?
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