Question 1082616
f'(x)=x*e^x+e^x=e^x(x+1)
f''(x)=e^x+(x+1)*e^x=e^x(1+x+1)=e^x(x+2)
This equal 0 only if x+2=0 or x=-2
graph of function and second derivative
{{{graph(300,300,-10,10,-1,10,x*exp(x),(x+2)*exp(x))}}}