Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter3: Linear And Nonlinear Functions
Section: Chapter Questions
Problem 26MCQ
Related questions
Question
![**Finding the Average Rate of Change**
For the function \( g(x) = -3x^2 - 2x \), determine the average rate of change from \( x = 4 \) to \( x = 8 \).
**Solution Steps:**
1. **Understand the Function**: The function given is \( g(x) = -3x^2 - 2x \).
2. **Evaluate the Function at Given Points**:
- \( g(4) = -3(4)^2 - 2(4) \)
- \( g(8) = -3(8)^2 - 2(8) \)
3. **Calculate the Average Rate of Change**:
- Use the formula:
\[
\frac{g(x_2) - g(x_1)}{x_2 - x_1}
\]
- Plug in the values for \( x_1 = 4 \) and \( x_2 = 8 \).
By following these steps, you can find the average rate of change of the function \( g(x) \) over the interval from \( x = 4 \) to \( x = 8 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9adcd2a-782c-4aec-98d2-41735c0afa7a%2F8a28ced2-8d32-4e30-95d7-c7dac3a46852%2F3fi9e3g.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Average Rate of Change**
For the function \( g(x) = -3x^2 - 2x \), determine the average rate of change from \( x = 4 \) to \( x = 8 \).
**Solution Steps:**
1. **Understand the Function**: The function given is \( g(x) = -3x^2 - 2x \).
2. **Evaluate the Function at Given Points**:
- \( g(4) = -3(4)^2 - 2(4) \)
- \( g(8) = -3(8)^2 - 2(8) \)
3. **Calculate the Average Rate of Change**:
- Use the formula:
\[
\frac{g(x_2) - g(x_1)}{x_2 - x_1}
\]
- Plug in the values for \( x_1 = 4 \) and \( x_2 = 8 \).
By following these steps, you can find the average rate of change of the function \( g(x) \) over the interval from \( x = 4 \) to \( x = 8 \).
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