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I was reading Haaser-Sullivan's Real Analysis and came across a problem for which I have a doubt. A part of it is stated like this : " For all x in the closed interval [a,b] in R, |g'(x)|<=1 '' (g(x) is, of course, a real-valued function of a real variable and that's all we know about it). Does that mean that for all x in [a,b], g'(x) is defined or that for all x in [a,b] such that g'(x) is defined, |g(x)|<=1?

Thanks in advance!

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# Reading Haaser-Sullivan's Real Analysis

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