This preview shows page 1. Sign up to view the full content.
Unformatted text preview: So, 3/2 is the value guaranteed by Rolle’s Theorem. The Mean Value Theorem: Let f be a function that satisfies the following: 1. f is continuous on the closed interval [a, b]. 2. f is differentiable on the open interval (a, b). Then there is a number c in ( a,b) such that ( ) ( ) ( ) f b f a f c b a′ =, or equivalently ( ) ( ) ( )( ) f b f a f c b a= ′Restated… …at some place c in [a, b], the instantaneous rate of change is equal to the average rate of change over the interval [a, b]. …at some time c between a and b, the instantaneous velocity is equal to the average velocity over the entire interval. Try exercises 2, 6, 14, 23 on pp 285286 in your text....
View
Full
Document
This note was uploaded on 12/12/2011 for the course MAC 2311 taught by Professor Teague during the Spring '11 term at Santa Fe College.
 Spring '11
 Teague
 Calculus, Mean Value Theorem

Click to edit the document details