# L23 - L23 Mean Value Theorem Rolles Theorem Let f be a...

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L23 – Mean Value Theorem Rolle’s Theorem – Let f be a function that satisfies the following properties: 1. 2. 3. The there is a c in ( a, b ) such that 1

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Graphically 2
Show that f ( x ) = x 3 + 3 x - 2 has exactly one real root. 3

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Find the value of c implied by Rolle’s Theorem for f ( x ) = (2 x - x 2 ) 2 3 on [ 0 , 2 ] . 4
Find the value of c implied by Rolle’s Theorem for g ( x ) = cos( πx ) on [ 0 , 2 ] . 5

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Mean Value Theorem – Let f be a function that satisfies 1. 2. Then there is a c in ( a, b ) such that 6
Equation of the secant line to f passing through ( a, f ( a ) ) and ( b, f ( b ) ) has slope: Equation – Consider h ( x ) = f ( x ) - y h ( x ) is 1. 2. 7

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h ( a ) = h ( b ) = By Rolle’s Theorem – 8
Find the value of c implied by the Mean Value Theorem for f ( x ) = x 3 - x 2 - 2 x on [ - 1 , 1 ] . 9

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The position of an object dropped from 650 ft is s ( t ) = 650 - 16 t

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