I'm having trouble finding the point of inflection of the graph

f(x)=(8e^x)/(e^(2x)+4)

so I cannot find the points of inflection even though I know the procedure:

f''(x)=(8e^x)/(e^(2x)+4)

f''(x)= 0 and f''(x) = undefined both do not exist...soo there is no point of inflection right? no.. there has to be BECAUSE, when i graph the function, concavity is changing.

from (-infinity, ln2) we have concave up and from (infinity,ln2) concave down. now... how do i find the point of inflection if i know that concavity is changing, but the second derivative does not allow me to find the point?

other info:

max point (ln2,2)

HA=y=0

yint=1.909