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 May 9th, 2017, 07:18 PM #1 Senior Member   Joined: Apr 2008 Posts: 192 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: USA Posts: 1,938 Thanks: 1006 $x_{inf} = 2-b$ $x > 0$ $x_{inf}>0 \Rightarrow 2-b > 0$ $b < 2$ Thanks from davedave
 May 10th, 2017, 03:41 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,160 Thanks: 866 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. Thanks from davedave
 May 11th, 2017, 10:31 AM #4 Senior Member   Joined: Apr 2008 Posts: 192 Thanks: 3 Thank you, romsek and Country Boy.

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