Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.)
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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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