Clay Kitchings :: EMAT 6600 :: Minimum of



Use the AM-GM inequality to show that the minimum of  is 2. 


AM-GM Inequality:      


Let a = 1/x and b = x


Apply AM-GM Inequality








Now for the “with equality” part:  1/x = x implies x =1 or -1.  The negative value does not satisfy the above inequality, but x=1 satisfies it. So let’s calculate f(1).  f(1) = 1/1 + 1 = 2.  So, this value will always be larger than or equal to 2, so therefore the minimum of the function is indeed 2.