Let F be the function given by f(x)= 2xe^x. Determine the interval(s) on which the graph is concave down.
1 answer:
Hello,
y=2xe^x
y'=2(e^x+xe^x)=2(x+1)e^x
y''=2(e^x+(x+1)e^x)=2(x+2)e^x
x |-infinite -2 0 +infinite
e^x | ++++++++++++++++++
x+2 |------------0 +++++++++++
y'' | -----------0 +++++++++++
y''<0 if x<-2
<span>The interval on which the graph is concave down is (-infinite -2[</span>
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