f is increasing when x<0 and 2 f is decreasing when 04.

f has local minimum at x=2 and local maximum at x=0 and x=4 because of the way it shifts between increasing and decreasing.

f is concave up when 13.

It has inflection points at x=1 and x=3.

f has the local maximum values at x=0 and x=4, and it has a local minimum value at x=2.