Look at the graph of f(x) = x² +1. What is the average rate of change between [-1,3]? 401 Look at the table below. What is the average rate of change between[-4,4]?. -4 -2 0 4 y 16 $4 0 16
Look at the graph of f(x) = x² +1. What is the average rate of change between [-1,3]? 401 Look at the table below. What is the average rate of change between[-4,4]?. -4 -2 0 4 y 16 $4 0 16
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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![**Graph and Table Analysis: Understanding the Average Rate of Change**
**Graph Analysis:**
The graph represents the function \( f(x) = x^2 + 1 \). You are asked to find the average rate of change between the interval \([-1, 3]\).
The graph is a parabola opening upwards with its vertex at the point (0, 1). To find the average rate of change, calculate the change in \( y \) values over the change in \( x \) values for the interval \([-1, 3]\).
**Table Analysis:**
A table is given with \( x \) and \( y \) values:
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-4 & 16 \\
-2 & 4 \\
0 & 0 \\
4 & 16 \\
\hline
\end{array}
\]
You need to calculate the average rate of change between the interval \([-4, 4]\) using the given table. To do this, use the formula for the average rate of change, which is the difference in \( y \) values divided by the difference in \( x \) values within the specified interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29e4da2c-5667-491c-b94b-db75d9eb231b%2Ff3f1ea7e-ff9a-403a-879e-8105dcaf4bb8%2Flh6wrgc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graph and Table Analysis: Understanding the Average Rate of Change**
**Graph Analysis:**
The graph represents the function \( f(x) = x^2 + 1 \). You are asked to find the average rate of change between the interval \([-1, 3]\).
The graph is a parabola opening upwards with its vertex at the point (0, 1). To find the average rate of change, calculate the change in \( y \) values over the change in \( x \) values for the interval \([-1, 3]\).
**Table Analysis:**
A table is given with \( x \) and \( y \) values:
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-4 & 16 \\
-2 & 4 \\
0 & 0 \\
4 & 16 \\
\hline
\end{array}
\]
You need to calculate the average rate of change between the interval \([-4, 4]\) using the given table. To do this, use the formula for the average rate of change, which is the difference in \( y \) values divided by the difference in \( x \) values within the specified interval.
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