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Unformatted text preview: 5 , . 6] and that the special case of Newtons method applies. [8] (c) Show that on the interval [0 . 5 , 1] one has  P ( x )  3 and  P 00 ( x )  12. [12] (d) Apply the special case of Newtons method to nd the root r from (b) to within 108 . 4. Solve the following inequalities: [5] (a)  x3  > 3 x + 2. [5] (b)  x  ( x 21) > 0. [5] (c) ( x3) ( x1) > x4. [4] 5. (a) State the Mean Value Theorem (MVT) for rational functions. Clearly indicate what are the hypotheses and what is the conclusion. [4] (b) Prove that MVT applies to f ( x ) = x (1+ x 2 ) on [0 , 10] and state its conclusion in this situation. [7] (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 numerical values of those z .) 2...
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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
 HIMONAS
 Calculus

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