Concept explainers
(a) Find the maximum value of
given that x1, x2, . . . , xn are positive numbers and x1 + x2 + . . . + xn = c, where c is a constant.
(b) Deduce from part (a) that if x1, x2, . . . , xn are positive numbers, then
This inequality says that the geometric mean of n numbers is no larger than the arithmetic mean of the numbers. Under what circumstances are these two means equal?
Want to see the full answer?
Check out a sample textbook solutionChapter 14 Solutions
Multivariable Calculus
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning