Which of the following statements is correct?

I made a mistake is the attachment .f is derivative not differentiabile . Sorry , english is not my first language ..
 
Having made 5 post before you should know by now that we need to see your work so that we know where to help you.
 
I doubt that it says that "f is derivative"; it makes sense to say "f is differentiable".

But the whole problem confuses me; it seems that the derivative f'(x) can never be less than -1, which doesn't fit with the stated limits, at least not to my intuition.

Can you show us the actual problem, in the original language, so we can check out the translation ourselves?
 
what i meant was that whatever x in the interval (a,b) exists f'(x) . The language is romanian
 

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Your original translation looks good to me. And I realize I misread something, so the problem is not nonsense. It is also not obvious, so we'll have to give it some thought!

Perhaps you can also do as Jomo asked, and tell us what ideas you have. Have you learned anything recently that this might be intended to exercise? Is there anything else that might help us know what help you need, and what methods are available?
 
i found the solution . this is actually from the University of Polytechnics Bucharest admission exam . Sorry i didn't found it earlier .
 

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