Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Topic: Calculating the Average Rate of Change**
**Graph Description:**
The graph shown is labeled \( y = f(x) \). It depicts a curve that initially decreases, then increases to a peak, and finally decreases sharply. Key points on the graph include:
- At \( x = 1 \), \( f(x) = 1 \).
- At \( x = 3 \), \( f(x) = 5 \).
**Objective:**
Determine the average rate of change of the function \( f(x) \) from \( x = 1 \) to \( x = 3 \).
**Calculation:**
The average rate of change is given by the formula:
\[
\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]
Plug in the values:
- \( f(3) = 5 \)
- \( f(1) = 1 \)
\[
\text{Average Rate of Change} = \frac{5 - 1}{3 - 1} = \frac{4}{2} = 2
\]
**Conclusion:**
The average rate of change of \( f(x) \) from \( x = 1 \) to \( x = 3 \) is 2.
**Multiple Choice Section:**
- \(-1\)
- **2**
- 5
- 3
- 1
- 0
The correct answer is highlighted: **2**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c72f5a5-765b-4af8-8c83-eae60846a923%2Fe57a7120-e014-449d-95e9-cea20c613051%2Fo5m7rdm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Calculating the Average Rate of Change**
**Graph Description:**
The graph shown is labeled \( y = f(x) \). It depicts a curve that initially decreases, then increases to a peak, and finally decreases sharply. Key points on the graph include:
- At \( x = 1 \), \( f(x) = 1 \).
- At \( x = 3 \), \( f(x) = 5 \).
**Objective:**
Determine the average rate of change of the function \( f(x) \) from \( x = 1 \) to \( x = 3 \).
**Calculation:**
The average rate of change is given by the formula:
\[
\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]
Plug in the values:
- \( f(3) = 5 \)
- \( f(1) = 1 \)
\[
\text{Average Rate of Change} = \frac{5 - 1}{3 - 1} = \frac{4}{2} = 2
\]
**Conclusion:**
The average rate of change of \( f(x) \) from \( x = 1 \) to \( x = 3 \) is 2.
**Multiple Choice Section:**
- \(-1\)
- **2**
- 5
- 3
- 1
- 0
The correct answer is highlighted: **2**.
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