if f'(x) > 0 for all real values of x then x increases without bounds. I thought that was true but in the back of the book it says false and uses f(x)=2x/sqrt(x(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}+2) as an example. i worked out the derivative and got f'(x) = 4/(x^{2}+2)^{3/2}.

how does that show that the first sentence is false? i'm quite confused abou this

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# Derivative increasing without bounds

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