graph of f '(x) is attached.

is this correct:

f is increasing on (3,6) and (6,8)

f is concave down on (0,1.5) and (4.5,6) and (6,9)

the critical numbers of f are x=0, x=3, x=6, x=8

the values of x that f has a local maximum is x=8

the values of x that f has a local minimum is x=3