If the function f(x)=(ln(x))/(x) where x>0, has a maximum at (e,1/e) compare the numbers e^(pi) and pi^(e).

Kameron Wang

Kameron Wang

Answered question

2022-11-17

If the function f ( x ) = l n ( x ) x where x>0, has a maximum at ( ( e , 1 e )) compare the numbers e π and π e
l n ( x ) is the natural logarithmic function i.e the logarithmic function with base e.

Answer & Explanation

jennasyliang4tr

jennasyliang4tr

Beginner2022-11-18Added 15 answers

Well, since f has a max at x=e, then
f ( e ) f ( x )
for all x in the domain of f. In particular, if x = π, then
f ( e ) > f ( π ) ln e e > ln π π π ln e > e ln π e π > π e

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