Is it possible to find a condition P so that f is bounded iff f' has P?

by Andrei Secuiu   Last Updated September 11, 2019 19:20 PM

Let's consider a differentiable function f:R->R, whose derivative is f'.

Is it possible to find a set of properties P so that f is bounded if and only if f' respects P? If so, do you know a theorem which states exactly who is P?

What I was able to find required more properties for f and f', meaning a loss of generality. For instance, if f' is strictly positive and f is bounded, then f' tends to 0.

I know f' is not necessarrily bounded, though that doesn't help much.

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