
concave
http://www.webassign.net/scalcet/431.gif
(c) The open interval on which f is concave upward.
(d) The open interval on which f is concave downward.
(e) The coordinates of the point of inflection.
i don't understand. isn't it concave upward at (2,4) http://www.mymathforum.com/images/smilies/icon_sad.gif

Change one word.
Concave up ON $\displaystyle (\infty,2)$
Concave down ON $\displaystyle (2,\infty)$
Your point (2,4) is the point of inflection.

If I am reading that graph correctly, (2, 4) isn't even on the graph. The inflection point is at (2, 3).

I'm not real clear on the concavity at (4,1), either. I can formulate an opinion if you tell me it is continuous, there. It's a problem with drawings. There is a little guess work involved.