# 6.7 Average Value Of A Functionap Calculus

The average value of f from x = a to x = b is the integral Discussion Using Flash Average value and the rate of change. Discussion Using Flash Geometrical. Where the sum is the result of adding all of the given numbers, and the count is the number of values being added. For example, given the 5 numbers, 2, 7, 19, 24, and 25, the average can be calculated as such.

Show Mobile Notice

Assignments AB 2020-2021. 1.09 Average Vs. Instantaneous Rates. 1.10 Secant, Tangent, and Normal Lines. Mean Value Theorem. Calculus: Early Transcendentals 8th Edition answers to Chapter 6 - Section 6.5 - Average Value of a Function - 6.5 Exercises - Page 463 7 including work step by step written by community members like you. Textbook Authors: Stewart, James, ISBN-10:, ISBN-13: 978-1-28574-155-0, Publisher: Cengage Learning. Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.

Show All NotesHide All Notes
You appear to be on a device with a 'narrow' screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.
Please do not email me to get solutions and/or answers to these problems. I will not give them out under any circumstances nor will I respond to any requests to do so. The intent of these problems is for instructors to use them for assignments and having solutions/answers easily available defeats that purpose.

### Section 6-1 : Average Function Value

For problems 1 – 4 determine ({f_{{rm{avg}}}}) for the function on the given interval.

1. (fleft( x right) = 8{x^4} - 7{x^3} + 2) on (left[ { - 2,1} right])
2. (fleft( x right) = left( {4 - x} right){{bf{e}}^{{x^{,2}} - 8x}}) on (left[ {1,4} right])
3. (fleft( x right) = 6x - frac{{4x}}{{{x^2} + 1}}) on (left[ { - 3,0} right])
4. (fleft( x right) = cos left( {3x} right){left[ {2 + sin left( {3x} right)} right]^4}) on (left[ {0,frac{pi }{6}} right])

### 6.7 Average Value Of A Functional Calculus 2nd Edition

For problems 5 – 8 find ({f_{{rm{avg}}}}) for the function on the given interval and determine the value of c in the given interval for which (fleft( c right) = {f_{{rm{avg}}}}).

### 6.7 Average Value Of A Functional Calculus Equation

1. (fleft( x right) = 10 - 4x - 6{x^2}) on (left[ {2,6} right])
2. (fleft( x right) = 7{x^2} + 2x - 3) on (left[ { - 1,1} right])
3. (fleft( x right) = 9 - 2{{bf{e}}^{4x + 1}}) on (left[ { - 1,2} right])
4. (fleft( x right) = 8 - cos left( {frac{x}{4}} right)) on (left[ {0,4pi } right])