Find the smallest value of x, for all x real of $(x+1)^{x} ≤ x^{(x+1)}$
I tried creating a function and evaluating the derivative, but it didn't work. Does anybody have an idea?
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use the link https://math.stackexchange.com/questions/871169/find-all-solutions-of-ab-ba – Jan 22 '20 at 19:22
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2that is equivalent to $\log (x+1)/(x+1) < \log x / x$. You can then study the function $\log x/x$. – Quang Hoang Jan 22 '20 at 19:22
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https://math.stackexchange.com/questions/116112/find-the-maximum-of-fx-x1-x – lab bhattacharjee Jan 22 '20 at 19:40
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The approx value is x= 2.29317 – almagest Jan 22 '20 at 20:00
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How did they get to 2.29? please – Killemal Jan 22 '20 at 23:32