Sorry for this long, but i seem to be getting half of these right.
f'' is positive when f is concave up x<-1 and x>6
f'' is negative when f is concave down 0
f''=0 when f is not concave up or concave down -1
Non-differentiable at x=-1 and x=0
If you find out that any of these are incorrect then please let me know but I think they are all ok. :)