1205-hwt0402-slides

# 1205-hwt0402-slides - Outline Math 1205 4.2 The Mean Value...

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Outline Math 1205 § 4.2: The Mean Value Theorem Heath David Hart Fall 2007 Heath David Hart Math 1205 § 4.2: The Mean Value Theorem

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Outline Table of Contents: Notes for Day 20: § 4.2: The Mean Value Theorem Heath David Hart Math 1205 § 4.2: The Mean Value Theorem
Outline Rolle’s Theorem Let f ( x ) be a function which is continuous on [ a , b ] and diﬀerentiable on ( a , b ) , with f ( a ) = f ( b ) . Then there is a number c in ( a , b ) where f 0 ( c ) = 0. Heath David Hart Math 1205 § 4.2: The Mean Value Theorem

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Outline Rolle’s Theorem In this example, we’re looking at a smooth curve, and f ( 2 ) = f ( 5 ) . Heath David Hart Math 1205 § 4.2: The Mean Value Theorem
Outline Rolle’s Theorem Rolle’s Theorem says that we can ﬁnd a point in the interval ( 2, 5 ) where the tangent line is horizontal. Heath David Hart Math 1205 § 4.2: The Mean Value Theorem

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Outline Rolle’s Theorem This should make sense: If a smooth function starts and ends at the same y -value, then either:
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1205-hwt0402-slides - Outline Math 1205 4.2 The Mean Value...

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