we have the function
[tex]f\mleft(x\mright)=xe^{\left(13x\right)}[/tex]
Find out the first derivative
[tex]f^{\prime}\mleft(x\mright)=e^{(13x)}+13xe^{(13x)}[/tex]
Find out the second derivative
[tex]f^{\prime}^{\prime}\left(x\right)=26e^{\left(13x\right)}+169xe^{\left(13x\right)}[/tex]
Equate the second derivative to zero, to find out the turning point or inflection point
[tex]26e^{\left(13x\right)}+169xe^{\left(13x\right)}=0[/tex]
the turning point is (-2/13,0)
therefore
Concave up -----> (-2/13, infinite)
Concave down ----> (-infinite, -2/13)
