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I know that in order for g to be increasing, its derivative must be positive. But, I have a hard time showing that its derivative is indeed positive.

Thank you!

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  • $\begingroup$ Can you find the derivative? $\endgroup$ Commented Oct 11, 2018 at 2:10
  • $\begingroup$ That's the idea, yes. $\endgroup$
    – Mik
    Commented Oct 11, 2018 at 2:13
  • $\begingroup$ What I meant was, do you know how to find the derivative? $\endgroup$ Commented Oct 11, 2018 at 2:14

1 Answer 1

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Hint:

By the Fundamental theorem of Calculus $$g'(x)=\frac{1}{x}f(x)-\frac{1}{x^2}\int_{0}^{x}f(t)dt=\frac{1}{x^2}\int_{0}^{x}f(x)-f(t)dt.$$

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    $\begingroup$ Yes, that's exactly what I have and I was also able to prove that it is positive for (0,∞). Thanks anyways! :) $\endgroup$
    – Mik
    Commented Oct 11, 2018 at 3:03

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