Find the coordinates of the inflection points for f(x)=xe^x?

1 Answer
Teddy
Jun 26, 2018

The inflection point for #f(x)=xe^x# is at #(-2, -2e^(-2))# or about #(-2, -.271)#.

Explanation:

The point(s) of inflection for a function #f# can be found by solving #f''=0#.
#f(x)=xe^x#
#:.f'(x)=e^x+xe^x#
#:. f''(x)=e^x+e^x+xe^x=e^x(x+2)#
The inflection point(s) are found by solving #e^x(x+2)=0#. Since #e^x# is always positive, we know that #x+2=0# or #x=-2# is the x-coordinate of the only inflection point. To find the y-coordinate, substitute #x=-2# into #f(x)# to get that the inflection point is located at #(-2, -2e^(-2))#.

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