Module 4 : Local / Global Maximum / Minimum and  Curve Sketching
Lecture 11 : Convex / Concave Functions [Section 11.2]
11.2.2 Example:
(i)
Consider the function
 

                  

For

                  
Hence,
                  
i.e., is strictly concave up in Similarly, it can be seen that is strictly concave down in . Further has a point of inflection at

Another way of describing the convexity / concavity is the following:

   
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