Range and Graph of a function Let $$f(x)=\left(1+\frac{1}{x}\right)^x$$
State the range and plot its graph wherever the function is defined.
I got the range and $f'(x)$, but I cannot find the sign of it to predict the increasing/decreasing of the graph. Please help.

Hint
$$f(x)=\left(1+\frac{1}{x}\right)^x\implies \log(f(x))=x \log\left(1+\frac{1}{x}\right)$$
$$\frac{f'(x)}{f(x)}=\log \left(1+\frac{1}{x}\right)-\frac{1}{x+1}$$ Now, play with some inequalities.
