Module 4 : Local / Global Maximum / Minimum and  Curve Sketching
Lecture 11 : Convex / Concave Functions [Section 11.2]
  These considerations motivate our next definition.
11.2.1 Definitions:
  Let .
(i)
  We say is concave upward (or convex) if for all
 

                           
that is, the chord joining lies on or above the graph of on . We say is strictly concave upward or strictly convex if the above inequality is strict.

(ii)
 We say that is a concave downward (or concave) function if for all ,
                             
 

that is, the chord joining lies on or below the graph of on . We say is strictly concave downward if the inequality above is strict.

(iii)
 We say has a point of inflection at if for some is strictly concave upward on
  is strictly concave downward on or vice versa. Thus, changes its nature of strict convexity/ concavity at a point of inflection.
   
 
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