Find the average rate of change for the given function. f(x)=x² + 10x between x = 0 and x = 8 The average rate of change is (Simplify your answer.)
Find the average rate of change for the given function. f(x)=x² + 10x between x = 0 and x = 8 The average rate of change is (Simplify your answer.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Find the Average Rate of Change for the Given Function**
Given function:
\[ f(x) = x^2 + 10x \]
We need to find the average rate of change between \( x = 0 \) and \( x = 8 \).
The formula for the average rate of change of a function \( f(x) \) over the interval \([a, b]\) is:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
In this case, substitute \( a = 0 \) and \( b = 8 \):
1. Calculate \( f(0) \):
\[
f(0) = 0^2 + 10(0) = 0
\]
2. Calculate \( f(8) \):
\[
f(8) = 8^2 + 10(8) = 64 + 80 = 144
\]
3. Apply the average rate of change formula:
\[
\text{Average Rate of Change} = \frac{144 - 0}{8 - 0} = \frac{144}{8} = 18
\]
The average rate of change is **18**.
(Simplify your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56289daf-944e-4934-ac7e-546f2acb04ad%2F7cb9f39a-4a1e-4781-8631-f0ce86c01b3b%2Flflaxv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the Average Rate of Change for the Given Function**
Given function:
\[ f(x) = x^2 + 10x \]
We need to find the average rate of change between \( x = 0 \) and \( x = 8 \).
The formula for the average rate of change of a function \( f(x) \) over the interval \([a, b]\) is:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
In this case, substitute \( a = 0 \) and \( b = 8 \):
1. Calculate \( f(0) \):
\[
f(0) = 0^2 + 10(0) = 0
\]
2. Calculate \( f(8) \):
\[
f(8) = 8^2 + 10(8) = 64 + 80 = 144
\]
3. Apply the average rate of change formula:
\[
\text{Average Rate of Change} = \frac{144 - 0}{8 - 0} = \frac{144}{8} = 18
\]
The average rate of change is **18**.
(Simplify your answer.)
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