Prove XXXXXXXXXXHint: Set a = s 2 , b = 2sδ/(16L2 ), c = 16L2 (1 + δ)s/3, and d = 2(1 + δ) 2 + δ(1 + δ)/3. Then the left-hand side of (7.8) is equal to f(σ2) where                               f(u) =...

Prove (7.8). Hint: Set

a = s 2 , b = 2sδ/(16L2 ), c = 16L2 (1 + δ)s/3, and d = 2(1 + δ) 2 + δ(1 + δ)/3.

Then the left-hand side of (7.8) is equal to f(σ2) where

                              f(u) = a + b · u c + d · u (u > 0).

Compute the derivative fof f and show

                             f (u) = 0 for all u > 0.

Use this to determine

                            min u>0 f(u)

by considering

                           f(0) and limu→∞ f(u).