15 A function f (x1, x2, . . . , xn) is quasi-concave on a convex set S  Rn if x  S, x  S, and 0  c  1 implies f [cx (1  c)x]  min[ f (x ), f (x)]

Show that if f is concave on R1, then f is quasi-concave.

Which of the functions in Figure 19 is quasi-concave? Is a quasi-concave function necessarily a concave function?