November 27th, 2015, 10:55 AM  #1 
Newbie Joined: Nov 2015 From: Canada Posts: 1 Thanks: 0  Shapes of graphs
How do I find the concavity of this function and its inflection points just by looking at it ? http://i.imgur.com/q9uavkv.png 
November 27th, 2015, 12:11 PM  #2 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
The function is convex wherever the graph opens upwards. For example, the part of the graph nearest the $x$axis is convex. Likewise, the function is concave wherever the graph opens downwards. For example, in the area in the middle. Inflection points are points where the graph switches from convex to concave (or vice versa). The first of these appears at what looks like the point (2, 5). 
November 27th, 2015, 01:05 PM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 3,044 Thanks: 1627 
check attachment ...


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