2 Find the average rate of change of g(x) = 6x³ + on the interval [-1, 1]. Enter your answer as either an integer or reduced fraction. > Next Question
2 Find the average rate of change of g(x) = 6x³ + on the interval [-1, 1]. Enter your answer as either an integer or reduced fraction. > Next Question
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Math Problem: Average Rate of Change**
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**Problem Statement:**
Find the average rate of change of \( g(x) = 6x^3 + \frac{2}{x^4} \) on the interval \([-1, 1]\).
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**Instructions:**
Enter your answer as either an integer or reduced fraction.
---
**Input Box:**
| |
|---|
---
**Navigation:**
\[ \rightarrow \text{Next Question} \]
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**Explanation of Average Rate of Change:**
To find the average rate of change of a function over an interval \([a, b]\), use the formula:
\[ \text{Average Rate of Change} = \frac{g(b) - g(a)}{b - a} \]
Here, \( g(x) = 6x^3 + \frac{2}{x^4} \), \( a = -1 \), and \( b = 1 \).
1. **Compute \( g(1) \):**
\[ g(1) = 6(1)^3 + \frac{2}{(1)^4} = 6 + 2 = 8 \]
2. **Compute \( g(-1) \):**
\[ g(-1) = 6(-1)^3 + \frac{2}{(-1)^4} = -6 + 2 = -4 \]
3. **Apply the formula:**
\[ \text{Average Rate of Change} = \frac{g(1) - g(-1)}{1 - (-1)} = \frac{8 - (-4)}{1 - (-1)} = \frac{8 + 4}{1 + 1} = \frac{12}{2} = 6 \]
Therefore, the average rate of change of \( g(x) \) on the interval \([-1, 1]\) is \( 6 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a66d878-2f58-4b17-a7a9-b61e2abefcf5%2F97fda490-f08b-4610-9146-d06c51cbd719%2Fax5fsxi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Math Problem: Average Rate of Change**
---
**Problem Statement:**
Find the average rate of change of \( g(x) = 6x^3 + \frac{2}{x^4} \) on the interval \([-1, 1]\).
---
**Instructions:**
Enter your answer as either an integer or reduced fraction.
---
**Input Box:**
| |
|---|
---
**Navigation:**
\[ \rightarrow \text{Next Question} \]
---
**Explanation of Average Rate of Change:**
To find the average rate of change of a function over an interval \([a, b]\), use the formula:
\[ \text{Average Rate of Change} = \frac{g(b) - g(a)}{b - a} \]
Here, \( g(x) = 6x^3 + \frac{2}{x^4} \), \( a = -1 \), and \( b = 1 \).
1. **Compute \( g(1) \):**
\[ g(1) = 6(1)^3 + \frac{2}{(1)^4} = 6 + 2 = 8 \]
2. **Compute \( g(-1) \):**
\[ g(-1) = 6(-1)^3 + \frac{2}{(-1)^4} = -6 + 2 = -4 \]
3. **Apply the formula:**
\[ \text{Average Rate of Change} = \frac{g(1) - g(-1)}{1 - (-1)} = \frac{8 - (-4)}{1 - (-1)} = \frac{8 + 4}{1 + 1} = \frac{12}{2} = 6 \]
Therefore, the average rate of change of \( g(x) \) on the interval \([-1, 1]\) is \( 6 \).
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