   Chapter 5, Problem 76RE ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Average Value of a Function In Exercises 71–76, find the average value of the function on the interval. Then find all x-values in the interval for which the function is equal to its average value. f ( x ) = 1 ( x + 5 ) 2 ;     [ − 1 , 6 ]

To determine

To calculate: The average value of function f(x)=1(x+5)2 on interval [1,6] and find all x-value in the interval for which the function f(x)=1(x+5)2 is equal to its average value.

Explanation

Given Information:

The provided function is f(x)=1(x+5)2 and interval is [1,6].

Formula used:

The average values of function f(x) over closed intervals [a,b] is given by,

Average values=1baabf(x)dx

The fundamental theorem of calculus:

abf(x)dx=F(b)F(a)

Here, F is function such that F(x)=f(x) for all x in [a,b].

Calculation:

Consider the function:

f(x)=1(x+5)2

Now apply the average values formula for function f(x)=1(x+5)2 over closed intervals [1,6]

Average values=16(1)16(1(x+5)2)dx=1716(x+5)2dx=17[(

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