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Determine the net change and the average rate of change for the function f(t) = t - 3t between t = 4 and t = 4 + h. net change average rate of change

Determine the net change and the average rate of change for the function f(t) = t - 3t between t = 4 and t = 4 + h. net change average rate of change

Advanced Engineering Mathematics
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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**Determine the net change and the average rate of change for the function** \( f(t) = t^2 - 3t \) **between** \( t = 4 \) **and** \( t = 4 + h \). - **Net change:** [ ] - **Average rate of change:** [ ] --- **Explanation of Task:** To solve the problem, calculate the net change and the average rate of change in the function \( f(t) \). 1. **Net Change:** - Calculate the difference in \( f(t) \) values at \( t = 4 + h \) and \( t = 4 \). - Formula: \( f(4 + h) - f(4) \). 2. **Average Rate of Change:** - Determine the rate of change by dividing the net change by the change in time, \( h \). - Formula: \(\frac{f(4 + h) - f(4)}{h}\). Place your answers in the provided boxes.
Transcribed Image Text:**Determine the net change and the average rate of change for the function** \( f(t) = t^2 - 3t \) **between** \( t = 4 \) **and** \( t = 4 + h \). - **Net change:** [ ] - **Average rate of change:** [ ] --- **Explanation of Task:** To solve the problem, calculate the net change and the average rate of change in the function \( f(t) \). 1. **Net Change:** - Calculate the difference in \( f(t) \) values at \( t = 4 + h \) and \( t = 4 \). - Formula: \( f(4 + h) - f(4) \). 2. **Average Rate of Change:** - Determine the rate of change by dividing the net change by the change in time, \( h \). - Formula: \(\frac{f(4 + h) - f(4)}{h}\). Place your answers in the provided boxes.
**Function and Inverse Graph Exercise** Below is a graph of a function \( f \). ### Description of the Function's Graph: - The graph is plotted on a standard coordinate plane with the horizontal axis labeled as \( x \) and the vertical axis labeled as \( y \). - The function \( f \) is represented by a red line connecting three main points: - The first point at \( (0, 0) \). - The second point at \( (3, 5) \). - The third point at \( (6, 10) \). - The line segments form a piecewise linear graph that increases continuously from left to right. ### Task: - Sketch the graph of \( f^{-1} \), the inverse of the function \( f \). *Note: When sketching the inverse of a function, swap the \( x \) and \( y \) values of each point to visualize how the graph would reflect over the line \( y = x \).*
Transcribed Image Text:**Function and Inverse Graph Exercise** Below is a graph of a function \( f \). ### Description of the Function's Graph: - The graph is plotted on a standard coordinate plane with the horizontal axis labeled as \( x \) and the vertical axis labeled as \( y \). - The function \( f \) is represented by a red line connecting three main points: - The first point at \( (0, 0) \). - The second point at \( (3, 5) \). - The third point at \( (6, 10) \). - The line segments form a piecewise linear graph that increases continuously from left to right. ### Task: - Sketch the graph of \( f^{-1} \), the inverse of the function \( f \). *Note: When sketching the inverse of a function, swap the \( x \) and \( y \) values of each point to visualize how the graph would reflect over the line \( y = x \).*
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