lecture23 - Lecture 23: Mean Value Theorem (Chapter 4, Sec....

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Unformatted text preview: Lecture 23: Mean Value Theorem (Chapter 4, Sec. 23) Rolles Theorem Let f be a function satisfying the following: 1) 2) 3) Then there is a number c in ( a;b ) such that Consider the graphs: 6- ? 6- ? 2 ex. Find the value of c implied by Rolles Theorem for f ( x ) = p 2 x x 2 on [0 ; 2]. 3 ex. Find the value of c implied by Rolles Theorem for f ( x ) = cos(2 x ) on [0 ; ]. 4 ex. Show that the equation x 3 + 6 x + 4 = 0 has exactly one real root. 5 We can use Rolles Theorem to prove the important Mean Value Theorem : Let f be a function that satisfles the following con- ditions: 1) 2) Then there is a number c in the interval ( a;b ) such that 6- ? 6 ex. Find the value of c implied by the Mean Value Theorem for f ( x ) = x 3 x 2 2 x on [ 1 ; 1]. 7 ex. The position of an object dropped from 800 ft is s ( t ) = 800 16 t 2 , where t is in seconds. Find the average velocity on the time interval [0 ; 5]....
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This note was uploaded on 05/17/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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lecture23 - Lecture 23: Mean Value Theorem (Chapter 4, Sec....

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