Explanation Given information: The figure is Formula used: The average value of f ( x ) 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 decreasing at x = 1 . ⇒ f ' ( 1 ) < 0 Hence, f ' ( 1 ) < 0 (b) The average value of f ( x ) on 0 ≤ x ≤ a 1 a − 0 ∫ 0 a f ( x ) d x = 1 a ∫ 0 a f ( x ) d x 1 a ∫ 0 a f ( x ) d x > 0 [ since ∫ 0 a f ( x ) d x > 0 ] Hence, 1 a ∫ 0 a f ( x ) d x > 0 (c) The average value of rate of change of f ( x ) for 0 ≤ x ≤ a is given by f a v g ' ( x ) = 1 a − 0 ∫ 0 a f ' ( x ) d x = 1 a ∫ 0 a f ' ( x ) d x = 1 a [

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 5.6, Problem 24P

To determine

To List the following numbers from least to greatest:

f'(1)

The average value of f(x) on 0≤x≤a .

The average value of rate of change of f(x), for 0≤x≤a .

∫0af(x)dx

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Chapter 5.6, Problem 23P

Chapter 5, Problem 1SYU

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Chapter 5 Solutions

APPLIED CALCULUS-PRINT COMPANION (LL)

Ch. 5.1 - Prob. 1P Ch. 5.1 - Prob. 2P Ch. 5.1 - Prob. 3P Ch. 5.1 - Prob. 4P Ch. 5.1 - Prob. 5P Ch. 5.1 - Prob. 6P Ch. 5.1 - Prob. 7P Ch. 5.1 - Prob. 8P Ch. 5.1 - Prob. 9P Ch. 5.1 - Prob. 10P

Ch. 5.1 - Prob. 11P Ch. 5.1 - Prob. 12P Ch. 5.1 - Prob. 13P Ch. 5.1 - Prob. 14P Ch. 5.1 - Prob. 15P Ch. 5.1 - Prob. 16P Ch. 5.1 - Prob. 17P Ch. 5.1 - Prob. 18P Ch. 5.1 - Prob. 19P Ch. 5.1 - Prob. 20P Ch. 5.1 - Prob. 21P Ch. 5.1 - Prob. 22P Ch. 5.1 - Prob. 23P Ch. 5.1 - Prob. 24P Ch. 5.1 - Prob. 25P Ch. 5.1 - Prob. 26P Ch. 5.1 - Prob. 27P Ch. 5.1 - Prob. 28P Ch. 5.1 - Prob. 29P Ch. 5.1 - Prob. 30P Ch. 5.1 - Prob. 31P Ch. 5.1 - Prob. 32P Ch. 5.1 - Prob. 33P Ch. 5.1 - Prob. 34P Ch. 5.1 - Prob. 35P Ch. 5.1 - Prob. 36P Ch. 5.1 - Prob. 37P Ch. 5.1 - Prob. 38P Ch. 5.1 - Prob. 39P Ch. 5.1 - Prob. 40P Ch. 5.1 - Prob. 41P Ch. 5.2 - Prob. 1P Ch. 5.2 - Prob. 2P Ch. 5.2 - Prob. 3P Ch. 5.2 - Prob. 4P Ch. 5.2 - Prob. 5P Ch. 5.2 - Prob. 6P Ch. 5.2 - Prob. 7P Ch. 5.2 - Prob. 8P Ch. 5.2 - Prob. 9P Ch. 5.2 - Prob. 10P Ch. 5.2 - Prob. 11P Ch. 5.2 - Prob. 12P Ch. 5.2 - Prob. 13P Ch. 5.2 - Prob. 14P Ch. 5.2 - Prob. 15P Ch. 5.2 - Prob. 16P Ch. 5.2 - Prob. 17P Ch. 5.2 - Prob. 18P Ch. 5.2 - Prob. 19P Ch. 5.2 - Prob. 20P Ch. 5.2 - Prob. 21P Ch. 5.2 - Prob. 22P Ch. 5.2 - Prob. 23P Ch. 5.2 - Prob. 24P Ch. 5.2 - Prob. 25P Ch. 5.2 - Prob. 26P Ch. 5.2 - Prob. 27P Ch. 5.2 - Prob. 28P Ch. 5.2 - Prob. 29P Ch. 5.2 - Prob. 30P Ch. 5.2 - Prob. 31P Ch. 5.2 - Prob. 32P Ch. 5.2 - Prob. 33P Ch. 5.2 - Prob. 34P Ch. 5.2 - Prob. 35P Ch. 5.2 - Prob. 36P Ch. 5.2 - Prob. 37P Ch. 5.2 - Prob. 38P Ch. 5.2 - Prob. 39P Ch. 5.2 - Prob. 40P Ch. 5.2 - Prob. 41P Ch. 5.2 - Prob. 42P Ch. 5.2 - Prob. 43P Ch. 5.3 - Prob. 1P Ch. 5.3 - Prob. 2P Ch. 5.3 - Prob. 3P Ch. 5.3 - Prob. 4P Ch. 5.3 - Prob. 5P Ch. 5.3 - Prob. 6P Ch. 5.3 - Prob. 7P Ch. 5.3 - Prob. 8P Ch. 5.3 - Prob. 9P Ch. 5.3 - Prob. 10P Ch. 5.3 - Prob. 11P Ch. 5.3 - Prob. 12P Ch. 5.3 - Prob. 13P Ch. 5.3 - Prob. 14P Ch. 5.3 - Prob. 15P Ch. 5.3 - Prob. 16P Ch. 5.3 - Prob. 17P Ch. 5.3 - Prob. 18P Ch. 5.3 - Prob. 19P Ch. 5.3 - Prob. 20P Ch. 5.3 - Prob. 21P Ch. 5.3 - Prob. 22P Ch. 5.3 - Prob. 23P Ch. 5.3 - Prob. 24P Ch. 5.3 - Prob. 25P Ch. 5.3 - Prob. 26P Ch. 5.3 - Prob. 27P Ch. 5.3 - Prob. 28P Ch. 5.3 - Prob. 29P Ch. 5.3 - Prob. 30P Ch. 5.3 - Prob. 31P Ch. 5.3 - Prob. 32P Ch. 5.3 - Prob. 33P Ch. 5.3 - Prob. 34P Ch. 5.3 - Prob. 35P Ch. 5.3 - Prob. 36P Ch. 5.3 - Prob. 37P Ch. 5.3 - Prob. 38P Ch. 5.3 - Prob. 39P Ch. 5.3 - Prob. 40P Ch. 5.4 - Prob. 1P Ch. 5.4 - Prob. 2P Ch. 5.4 - Prob. 3P Ch. 5.4 - Prob. 4P Ch. 5.4 - Prob. 5P Ch. 5.4 - Prob. 6P Ch. 5.4 - Prob. 7P Ch. 5.4 - Prob. 8P Ch. 5.4 - Prob. 9P Ch. 5.4 - Prob. 10P Ch. 5.4 - Prob. 11P Ch. 5.4 - Prob. 12P Ch. 5.4 - Prob. 13P Ch. 5.4 - Prob. 14P Ch. 5.4 - Prob. 15P Ch. 5.4 - Prob. 16P Ch. 5.4 - Prob. 17P Ch. 5.4 - Prob. 18P Ch. 5.4 - Prob. 19P Ch. 5.4 - Prob. 20P Ch. 5.4 - Prob. 21P Ch. 5.4 - Prob. 22P Ch. 5.4 - Prob. 23P Ch. 5.4 - Prob. 24P Ch. 5.4 - Prob. 25P Ch. 5.4 - Prob. 26P Ch. 5.4 - Prob. 27P Ch. 5.4 - Prob. 28P Ch. 5.4 - Prob. 29P Ch. 5.4 - Prob. 30P Ch. 5.4 - Prob. 31P Ch. 5.4 - Prob. 32P Ch. 5.4 - Prob. 33P Ch. 5.4 - Prob. 34P Ch. 5.4 - Prob. 35P Ch. 5.4 - Prob. 36P Ch. 5.4 - Prob. 37P Ch. 5.4 - Prob. 38P Ch. 5.4 - Prob. 39P Ch. 5.4 - Prob. 40P Ch. 5.4 - Prob. 41P Ch. 5.4 - Prob. 42P Ch. 5.4 - Prob. 43P Ch. 5.4 - Prob. 44P Ch. 5.5 - Prob. 1P Ch. 5.5 - Prob. 2P Ch. 5.5 - Prob. 3P Ch. 5.5 - Prob. 4P Ch. 5.5 - Prob. 5P Ch. 5.5 - Prob. 6P Ch. 5.5 - Prob. 7P Ch. 5.5 - Prob. 8P Ch. 5.5 - Prob. 9P Ch. 5.5 - Prob. 10P Ch. 5.5 - Prob. 11P Ch. 5.5 - Prob. 12P Ch. 5.5 - Prob. 13P Ch. 5.5 - Prob. 14P Ch. 5.5 - Prob. 15P Ch. 5.5 - Prob. 16P Ch. 5.5 - Prob. 17P Ch. 5.5 - Prob. 18P Ch. 5.5 - Prob. 19P Ch. 5.5 - Prob. 20P Ch. 5.5 - Prob. 21P Ch. 5.5 - Prob. 22P Ch. 5.5 - Prob. 23P Ch. 5.5 - Prob. 24P Ch. 5.5 - Prob. 25P Ch. 5.5 - Prob. 26P Ch. 5.5 - Prob. 27P Ch. 5.6 - Prob. 1P Ch. 5.6 - Prob. 2P Ch. 5.6 - Prob. 3P Ch. 5.6 - Prob. 4P Ch. 5.6 - Prob. 5P Ch. 5.6 - Prob. 6P Ch. 5.6 - Prob. 7P Ch. 5.6 - Prob. 8P Ch. 5.6 - Prob. 9P Ch. 5.6 - Prob. 10P Ch. 5.6 - Prob. 11P Ch. 5.6 - Prob. 12P Ch. 5.6 - Prob. 13P Ch. 5.6 - Prob. 14P Ch. 5.6 - Prob. 15P Ch. 5.6 - Prob. 16P Ch. 5.6 - Prob. 17P Ch. 5.6 - Prob. 18P Ch. 5.6 - Prob. 19P Ch. 5.6 - Prob. 20P Ch. 5.6 - Prob. 21P Ch. 5.6 - Prob. 22P Ch. 5.6 - Prob. 23P Ch. 5.6 - Prob. 24P Ch. 5 - Prob. 1SYU Ch. 5 - Prob. 2SYU Ch. 5 - Prob. 3SYU Ch. 5 - Prob. 4SYU Ch. 5 - Prob. 5SYU Ch. 5 - Prob. 6SYU Ch. 5 - Prob. 7SYU Ch. 5 - Prob. 8SYU Ch. 5 - Prob. 9SYU Ch. 5 - Prob. 10SYU Ch. 5 - Prob. 11SYU Ch. 5 - Prob. 12SYU Ch. 5 - Prob. 13SYU Ch. 5 - Prob. 14SYU Ch. 5 - Prob. 15SYU Ch. 5 - Prob. 16SYU Ch. 5 - Prob. 17SYU Ch. 5 - Prob. 18SYU Ch. 5 - Prob. 19SYU Ch. 5 - Prob. 20SYU Ch. 5 - Prob. 21SYU Ch. 5 - Prob. 22SYU Ch. 5 - Prob. 23SYU Ch. 5 - Prob. 24SYU Ch. 5 - Prob. 25SYU Ch. 5 - Prob. 26SYU Ch. 5 - Prob. 27SYU Ch. 5 - Prob. 28SYU Ch. 5 - Prob. 29SYU Ch. 5 - Prob. 30SYU Ch. 5 - Prob. 31SYU Ch. 5 - Prob. 32SYU Ch. 5 - Prob. 33SYU Ch. 5 - Prob. 34SYU Ch. 5 - Prob. 35SYU Ch. 5 - Prob. 36SYU Ch. 5 - Prob. 37SYU Ch. 5 - Prob. 38SYU Ch. 5 - Prob. 39SYU Ch. 5 - Prob. 40SYU Ch. 5 - Prob. 41SYU Ch. 5 - Prob. 42SYU Ch. 5 - Prob. 43SYU Ch. 5 - Prob. 44SYU Ch. 5 - Prob. 45SYU Ch. 5 - Prob. 46SYU Ch. 5 - Prob. 47SYU Ch. 5 - Prob. 48SYU Ch. 5 - Prob. 49SYU Ch. 5 - Prob. 50SYU Ch. 5 - Prob. 51SYU Ch. 5 - Prob. 52SYU Ch. 5 - Prob. 53SYU Ch. 5 - Prob. 54SYU Ch. 5 - Prob. 55SYU Ch. 5 - Prob. 56SYU Ch. 5 - Prob. 57SYU Ch. 5 - Prob. 58SYU Ch. 5 - Prob. 59SYU Ch. 5 - Prob. 60SYU Ch. 5 - Prob. 1FOT Ch. 5 - Prob. 2FOT Ch. 5 - Prob. 3FOT Ch. 5 - Prob. 4FOT Ch. 5 - Prob. 5FOT Ch. 5 - Prob. 6FOT Ch. 5 - Prob. 7FOT Ch. 5 - Prob. 8FOT Ch. 5 - Prob. 9FOT Ch. 5 - Prob. 10FOT Ch. 5 - Prob. 11FOT

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To List the following numbers from least to greatest: f ' ( 1 ) The average value of f ( x ) on 0 ≤ x ≤ a . The average value of rate of change of f ( x ) , for 0 ≤ x ≤ a . ∫ 0 a f ( x ) d x

Solution Summary: The author calculates the value of f(x) on the interval from a to b.

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To List the following numbers from least to greatest:

f'(1)

The average value of f(x) on 0≤x≤a .

The average value of rate of change of f(x), for 0≤x≤a .

∫0af(x)dx

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Chapter 5 Solutions

To List the following numbers from least to greatest: f ' ( 1 ) The average value of f ( x ) on 0 ≤ x ≤ a . The average value of rate of change of f ( x ) , for 0 ≤ x ≤ a . ∫ 0 a f ( x ) d x

Solution Summary: The author calculates the value of f(x) on the interval from a to b.

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To List the following numbers from least to greatest: f'(1) The average value of f(x) on 0≤x≤a . The average value of rate of change of f(x), for 0≤x≤a . ∫0af(x)dx

Want to see the full answer?

Chapter 5 Solutions

To List the following numbers from least to greatest:

f'(1)

The average value of f(x) on 0≤x≤a .

The average value of rate of change of f(x), for 0≤x≤a .

∫0af(x)dx