Calculus

Abstract

The values xi are thus all equal at an extrema. The constraint equation tells us that xi = 1/n, from which we deduce the desired result. This extrema corresponds to a maximum because the continuous function h must achieve both its maximum and minimum value on the compact set [0, 1] and we have already eliminated the minimum by introducing the restriction that the xi are nonzero. (b) Use part (a) to prove, for any n positive numbers ai, i = 1, . . . , n, that