Explanation Given information: The graph of f ' ( x ) i s Formula used: If f ( x ) is a function and the area between the two points with x = a and x = b is given by Area = ∫ a b | f ( x ) | d x Fundamental theorem of calculus : If f is continuous on the closed interval [ a , b ] and F is the indefinite integral of f on [ a , b ] , then ∫ a b f ( x ) d x = F ( b ) − F ( a ) For any two numbers x < y , x < x + y 2 < y . Calculation: We have the formula for area as Area = ∫ a b | f ( x ) | d x (1) And from the fundamental theorem ∫ a b f ( x ) d x = F ( b ) − F ( a ) (2) Combining (1) and (2), we have A r e a = F ( b ) − F ( a ) Let A 1 = Area under the curve and between x = 2 , 3 . A 2 = Area under the curve and between x = 3 , 4

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 6.1, Problem 40P

To determine

To list:The following in increasing order: f(4)−f(2)2,f(3)−f(2),f(4)−f(3) .

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Chapter 6.1, Problem 39P

Chapter 6.1, Problem 41P

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Chapter 6 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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The following in increasing order: f ( 4 ) − f ( 2 ) 2 , f ( 3 ) − f ( 2 ) , f ( 4 ) − f ( 3 ) .

Solution Summary: The author lists the following in increasing order: f'(x)is Formula used to calculate the area between the two points.

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To list:The following in increasing order: f(4)−f(2)2,f(3)−f(2),f(4)−f(3) .

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Chapter 6 Solutions