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....
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 Spring '11
 Teague
 Calculus, Topology, Derivative, Mean Value Theorem, Continuous function, Metric space, Rolle’s Theorem, Rolle

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