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: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

See similar textbooks

Concept explainers

Exponential Growth Model

The relation that represents an exponential function is:

Videos

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.6, Problem 23P

Chapter 5, Problem 1SYU

Chapter 5 Solutions

EBK APPLIED CALCULUS, ENHANCED ETEXT

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

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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.

Concept explainers

Videos

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 . ∫ 0 a f ( x ) d x

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

Concept explainers

Videos

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