Here is a review problem I have used in my class to help prepare students for the AP exam.
a) Find where f is increasing.
b) Find all relative max.
c) Find all relative min.
d) Find where f is concave down.
In part d, when x=0, f " does not exist and f(0) does.Thus at x=0 there is a possible point of inflection. After testing an x<0 and an x>0 it can be determined that f is concave down on both intevals. Is it a true statement to say that f is concave on the entire domain or must x=0 be excluded?