Question

Let F be the function given by f(x)= 2xe^x. Determine the interval(s) on which the graph is concave down.

Answer 1

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
The interval on which the graph is concave down is (-infinite -2[