6.5 This exercise is regarding Example 6.1 (continued) in Section 6.3. (i) Show that the function (u) is maximized at u = c, and

6.5 This exercise is regarding Example 6.1 (continued) in Section 6.3.

(i) Show that the function ψ(u) is maximized at u =

√

c, and the maximum is (1 +

√

c)

−2.

(ii) Show that the right side of (6.29) is minimized when bi = 1 + ai , which is greater than

√

ai , and the minimum is 4{π(1 + ai )}−1.