# Graph of a function

• February 22nd 2009, 01:04 AM
vance
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!
• February 22nd 2009, 01:57 AM
running-gag
Hi

$f(x) = x\:2^x = x\:e^{2\ln x}$

$f'(x) = e^{2\ln x} (1 + x \ln 2)$

Therefore f is decreasing from $-\infty$ to $-\frac{1}{\ln 2}$ and increasing from $-\frac{1}{\ln 2}$ to $+\infty$

The minimum has coordinates $(-\frac{1}{\ln 2} ; -\frac{1}{e\:\ln 2})$

The limit in $-\infty$ is 0 which shows that x-axis is an asymptot

The limit in $+\infty$ is $+\infty$

http://nsa05.casimages.com/img/2009/...5805782962.jpg