Is the logarithm of increasing (not necessarily strictly) function is concave?

Zackary Diaz

Zackary Diaz

Answered question

2022-11-14

Is the logarithm of increasing (not necessarily strictly) function is concave?

Answer & Explanation

Incampo5in

Incampo5in

Beginner2022-11-15Added 10 answers

No. Take any non-concave increasing function g and take the function f ( x ) = e g ( x )
Then:
f ( x ) is an increasing function, because x e x is increasing, and g is increasing.
x log ( f ( x ) ) is actually the function g, so it is not concave.

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