Let
                
We want to find regions of convexity/ concavity and points of inflection of . First of all, we note that is a continuous function and is not differentiable at the points and .

Since,
              

we have,
               

Thus,

              
Hence,
             is strictly concave up in the intervals

In the interval ,

             
Hence,
            is strictly concave down in

Since changes its nature from convexity to concavity at and from concavity to convexity at

            has points of inflection at