For the function, find all points of inflection or determine that no such points exist.
f (x) = x lnx for x > > 0
f (x) = x lnx for x > 0
The first derivative is
and the second derivative is
The second derivative is never zero, and is undefined only for x = 0. However, x = 0 isn't in the domain of the function anyway, so it can't be an IP. Thisfunction has no inflection points, which makes sense because it appears to be concave up the whole way: