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
Òwith equalityÓ part: 1/x = x
implies x =1 or -1. The negative
value does not satisfy the above inequality, but x=1 satisfies it. So letÕs
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.