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
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-> 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
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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.
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
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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/
