May 9th, 2017, 07:18 PM  #1 
Senior Member Joined: Apr 2008 Posts: 176 Thanks: 3  how to find inflection points
I have a lot of trouble with this problem. (ex) Consider the function g(x) = x*e^(x) + b*e^(x) where b is a constant. Find all values of b if any for which the graph of g has a point of inflection in 0 < x < infinity. my attempt The second derivative of g is g''(x) =  e^(x) (x  (2  b)) Setting g''(x) = 0 and solving for x give x= 2  b. Now, I have a problem. I cannot find b because there are two unknowns, which are x and b. Can someone explain how to do it? Thanks. 
May 9th, 2017, 08:14 PM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,497 Thanks: 755 
$x_{inf} = 2b$ $x > 0$ $x_{inf}>0 \Rightarrow 2b > 0$ $b < 2$ 
May 10th, 2017, 03:41 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,731 Thanks: 707 
The problem did not ask you to find a value of b, it asks you to find all values of b for which x is greater than 0. In other words, solve x= 2 b> 0.

May 11th, 2017, 10:31 AM  #4 
Senior Member Joined: Apr 2008 Posts: 176 Thanks: 3 
Thank you, romsek and Country Boy.


Tags 
find, inflection, points 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Concavity and Points of Inflection  gaz  Calculus  5  April 28th, 2017 03:55 AM 
Concavity and Points of Inflection  math999  Calculus  2  April 13th, 2013 07:09 PM 
inflection points analysis  m.nikolov  Calculus  2  January 12th, 2013 02:47 PM 
inflection points  cheyb93  Calculus  4  November 8th, 2012 11:30 AM 
inflection points  stainsoftime  Calculus  3  December 15th, 2008 12:19 AM 