Throughout the problems, let f(x) and g(x) be quasiconcave and defined on the same convex set in n-space, and let m(t) be a strictly increasing function of a single variable, defined for all real t.
- Is m quasiconcave? Strictly quasiconcave? Quasiconvex? Strictly quasiconvex?
- Which of the following functions must be quasiconcave on their domains?
max{f(x), g(x)}
min{f(x), g(x)}
f(-x)
m(f(x))
(tricky?) f(x) + g(x) - Fix two points u and v. Define h(t) = f(tu+(1-t)v) for t between 0 and 1 (again, f is quasiconcave).
Is the claim "h must be either nonincreasing in t or nondecreasing in t" true or false?