This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: 5 , . 6] and that the special case of Newtons method applies.  (c) Show that on the interval [0 . 5 , 1] one has | P ( x ) | 3 and | P 00 ( x ) | 12.  (d) Apply the special case of Newtons method to nd the root r from (b) to within 10-8 . 4. Solve the following inequalities:  (a) | x-3 | > 3 x + 2.  (b) | x | ( x 2-1) > 0.  (c) ( x-3) ( x-1) > x-4.  5. (a) State the Mean Value Theorem (MVT) for rational functions. Clearly indi-cate what are the hypotheses and what is the conclusion.  (b) Prove that MVT applies to f ( x ) = x (1+ x 2 ) on [0 , 10] and state its conclusion in this situation.  (c) For how many points z (0 , 10) does the conclusion of MVT hold for the function f and the interval given in (b)? (You need not determine the nu-merical values of those z .) 2...
View Full Document
This note was uploaded on 03/04/2012 for the course MATH 10250 taught by Professor Himonas during the Fall '08 term at Notre Dame.
- Fall '08