
Graph of a function
List all the asymptotes of the graph of the function and the approximate coordinates of each local extremum.
f(x)=x(2^x)
I've had a hard time trying to solve this graph , I used my graphing calculator, but it didn't help me.
Acording to my book, the negative x axis is an asymptote. Can someone explain me how to interpret and graph the function properly? Thanks in advance!

Hi
$\displaystyle f(x) = x\:2^x = x\:e^{2\ln x}$
$\displaystyle f'(x) = e^{2\ln x} (1 + x \ln 2)$
Therefore f is decreasing from $\displaystyle \infty$ to $\displaystyle \frac{1}{\ln 2}$ and increasing from $\displaystyle \frac{1}{\ln 2}$ to $\displaystyle +\infty$
The minimum has coordinates $\displaystyle (\frac{1}{\ln 2} ; \frac{1}{e\:\ln 2})$
The limit in $\displaystyle \infty$ is 0 which shows that xaxis is an asymptot
The limit in $\displaystyle +\infty$ is $\displaystyle +\infty$
http://nsa05.casimages.com/img/2009/...5805782962.jpg