Explanation Given information: The figure is Formula used: The average value of f on the interval from a to b = 1 b − a ∫ a b f ( x ) d x . Calculation: (a) From the figure, we can observe that f ( x ) is having minima at x = 1 so, derivative at x = 1 will be zero. Hence, f ' ( 1 ) = 0 (b) The average value of f on 0 ≤ x ≤ 4 is calculated below. Average = 1 4 − 0 ∫ 0 4 f ( x ) d x = 1 4 { ∫ 0 2 f ( x ) d x + ∫ 2 4 f ( x ) d x } > 0 Hence, 1 4 ∫ 0 4 f ( x ) d x > 0 (c) From the figure, we can observe that the area over 0 ≤ x ≤ 1 is decreasing, therefore ∫ 0 1 f ( x ) d x will be negative

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 5.6, Problem 23P

To determine

Tolist the following numbers from least to greatest:

f'(1)

The average value of f on 0≤x≤4 .

∫01f(x)dx

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Chapter 5.6, Problem 22P

Chapter 5.6, Problem 24P

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Chapter 5 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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Tolist the following numbers from least to greatest: f ' ( 1 ) The average value of f on 0 ≤ x ≤ 4 . ∫ 0 1 f ( x ) d x

Solution Summary: The author explains the formula used to calculate the average value of f on the interval from a to b.

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Tolist the following numbers from least to greatest:

f'(1)

The average value of f on 0≤x≤4 .

∫01f(x)dx

Want to see the full answer?

Chapter 5 Solutions

Tolist the following numbers from least to greatest: f ' ( 1 ) The average value of f on 0 ≤ x ≤ 4 . ∫ 0 1 f ( x ) d x

Solution Summary: The author explains the formula used to calculate the average value of f on the interval from a to b.

Videos

Tolist the following numbers from least to greatest: f'(1) The average value of f on 0≤x≤4 . ∫01f(x)dx

Want to see the full answer?

Chapter 5 Solutions

Tolist the following numbers from least to greatest:

f'(1)

The average value of f on 0≤x≤4 .

∫01f(x)dx