I had asked a question here, that sought to comment about the increasing/decreasing nature of $f(x)=\left(1+\frac1x\right)^{x}$ and $g(x)=\left(1+\frac1x\right)^{x+1}$. While I got a reply for the former, not for the latter.
$\left(1+\frac1x\right)^{x+1}=\left(1+\frac1x\right)^{x}\left(1+\frac1x\right)=$increasing function $\times$ decreasing function.
Also, $g'(x)=f'(x)\left(1+\frac1x\right)+f(x)\cdot-\frac1{x^2}=(+ve)\times(+ve)+(+ve)\times(-ve)$
Not able to conclude anything. Can you help? Thanks.
