SOLUTION: Hi guys! How are you all doing tonight? I am having a difficulty solving this problem and forgive me if I post my topic in the wrong section. f(x) = xe^x a) Determine the inte

Question 181425: Hi guys! How are you all doing tonight? I am having a difficulty solving this problem and forgive me if I post my topic in the wrong section.
f(x) = xe^x
a) Determine the intervals on which f is strictly increasing or decreasing.

b)Determine the extreme value of f.

c) Determine the intervals of concavity and of convexity and the inflexion points.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
f(x) = xe^x
a) Determine the intervals on which f is strictly increasing or decreasing.
f(x) is decreasing for x<-1
f(x) is increasing for x>-1 (the minimum is at x = -1)
b)Determine the extreme value of f.
f(x) = 0 as x approaches -infinity
f(x) approaches +infinity as x increases
c) Determine the intervals of concavity and of convexity and the inflexion points.
f'(x) = xe^x + e^x
e^x(x+1) = 0 (1st derivative = 0)
x = -1 is a minimum
--------------
f'' = xe^x + 2e^x
e^x(x+2) = 0 (2nd derivative = 0)
x = -2 is the point of inflection
You can see this clearly if you DL the software from http://www.padowan.dk/graph/

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