6.5 This exercise is regarding Example 6.1 (continued) in Section 6.3. (i) Show that the function (u)

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.