This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ± . ▀ 1 Note that these proofs can be found in Chapter 3 of Simon & Blume (1994). Theorem 3.5 Suppose that: (a) the domain of ± is an interval ² (finite or infinite) in » ¼ (b) g G is a local maximum of ± , and (c) g G is the only critical point of ± on ² . Then, g G is the global maximum of f on ² . Theorem 3.5 If ± is a ½ ¾ function whose domain is an interval ² and if ± ¸¸ is never zero on ² , then ± has at most one critical point in ² . This critical point is a global minimum if ± ¸¸ ¶ 0 , and a global maximum if ± ¸¸ º 0 . Theorem 3.2 Let ± be a ½ ¼ function on domain ¿ À Á . If ± ¸ ¶ 0 ( ± ¸ º 0µ on interval ´Â, Ãµ À ¿ , then ± is increasing (decreasing) on ´Â, Ãµ. If ± is increasing (decreasing) on ´Â, Ãµ , then ± ¸ Ä 0 ( ± ¸ Å 0µ on ´Â, Ãµ . A good answer to question 1: 2...
View
Full
Document
This note was uploaded on 05/26/2010 for the course ECON 475 taught by Professor Voyvoda during the Spring '10 term at Middle East Technical University.
 Spring '10
 voyvoda
 Economics

Click to edit the document details