Explanation Given information: F ( 0 ) = 3. The given graph of F ' is 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 ) 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 ) From the graph, we have, In the interval [ 0 , 2 ] , F ' ( t ) ≥ 0 a n d A r e a = 5. ⇒ 5 = F ( 2 ) − F ( 0 ) ⇒ F ( 2 ) = F ( 0 ) + 5 = 3 + 5 ( F ( 0 ) = 3 ) = 8 In the interval [ 2 , 5 ] , F ' ( t ) ≤ 0 a n d A r e a = 16

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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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 6.1, Problem 32P

To determine

To graph:

F(t) and to find the values of F(2),F(5),F(6).

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Chapter 6.1, Problem 31P

Chapter 6.1, Problem 33P

Chapter 6 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

Ch. 6.1 - Prob. 1P Ch. 6.1 - Prob. 2P Ch. 6.1 - Prob. 3P Ch. 6.1 - Prob. 4P Ch. 6.1 - Prob. 5P Ch. 6.1 - Prob. 6P Ch. 6.1 - Prob. 7P Ch. 6.1 - Prob. 8P Ch. 6.1 - Prob. 9P Ch. 6.1 - Prob. 10P

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To graph: F ( t ) and to find the values of F ( 2 ) , F ( 5 ) , F ( 6 ) .

Solution Summary: The author explains how to find the values of F(2), F(5), and F(6).

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To graph:

F(t) and to find the values of F(2),F(5),F(6).

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Chapter 6 Solutions

To graph: F ( t ) and to find the values of F ( 2 ) , F ( 5 ) , F ( 6 ) .

Solution Summary: The author explains how to find the values of F(2), F(5), and F(6).

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To graph: F(t) and to find the values of F(2),F(5),F(6).

Want to see the full answer?

Chapter 6 Solutions

To graph:

F(t) and to find the values of F(2),F(5),F(6).