Module 4 : Local / Global Maximum / Minimum and  Curve Sketching
Lecture 11 : Convex / Concave Functions [Section 11.2]
 

            

Thus, we can draw the following conclusions:

(i)
Since
 

         is strictly increasing on
Also,
        is strictly decreasing on          

(ii)
Since,
              is strictly concave downward on

Also,
          is strictly concave upward on
(iii)
By (i),

           has a local maximum at the point
    and
          has a local minimum at the point

(iv)
Also by (ii), since changes its nature from concave downward to concave upward at this point as
 

increases,
            has a point of inflection at
In view of the above, the graph of the function may be sketched as follows:

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