Module 4 : Local / Global Maximum / Minimum and  Curve Sketching
Lecture 11 : Convex / Concave Functions [Section 11.2]
11.2.10 Examples:
(i)
 Let .
 

Then
and
                       
Since such that such that
Thus,
                       is concave down for
                      is concave up for
Further,
has points of inflection at

(ii)
 Let
                         
The function is not differentiable at
1
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