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Match each interval with the corresponding rate of change for the function f(x) graphed below.

Match each interval with the corresponding rate of change for the function f(x) graphed below.

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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### Match each interval with the corresponding rate of change for the function f(x) graphed below. #### Graph Description: The graph provided is a plot of a polynomial function \( f(x) \) on a coordinate plane, with the x-axis ranging from -6 to 6 and the y-axis ranging from -6 to 6. The function exhibits several turning points and changes in the rate of change. #### Matching Intervals with Rate of Change: Below the graph, there is a list of intervals on the left side and corresponding rates of change on the right side. You need to match each interval with the appropriate rate of change for \( f(x) \). **Intervals:** - \( \boxed{\text{ }} \) from \( x = -1 \) to \( x = 0 \) - \( \boxed{\text{ }} \) from \( x = -2 \) to \( x = 1 \) - \( \boxed{\text{ }} \) from \( x = -1 \) to \( x = 2 \) - \( \boxed{\text{ }} \) from \( x = 0 \) to \( x = 1 \) - \( \boxed{\text{ }} \) from \( x = 1 \) to \( x = 2 \) - \( \boxed{\text{ }} \) from \( x = -3 \) to \( x = -2 \) **Rates of Change:** 1. -3 2. -2 3. -1 4. 0 5. 1 6. 2 7. 3 8. 4 To match an interval with its rate of change, compare the corresponding section of the graph and determine whether the function is increasing or decreasing, and by how much. The rate of change is the slope of the function over the given interval.
Transcribed Image Text:### Match each interval with the corresponding rate of change for the function f(x) graphed below. #### Graph Description: The graph provided is a plot of a polynomial function \( f(x) \) on a coordinate plane, with the x-axis ranging from -6 to 6 and the y-axis ranging from -6 to 6. The function exhibits several turning points and changes in the rate of change. #### Matching Intervals with Rate of Change: Below the graph, there is a list of intervals on the left side and corresponding rates of change on the right side. You need to match each interval with the appropriate rate of change for \( f(x) \). **Intervals:** - \( \boxed{\text{ }} \) from \( x = -1 \) to \( x = 0 \) - \( \boxed{\text{ }} \) from \( x = -2 \) to \( x = 1 \) - \( \boxed{\text{ }} \) from \( x = -1 \) to \( x = 2 \) - \( \boxed{\text{ }} \) from \( x = 0 \) to \( x = 1 \) - \( \boxed{\text{ }} \) from \( x = 1 \) to \( x = 2 \) - \( \boxed{\text{ }} \) from \( x = -3 \) to \( x = -2 \) **Rates of Change:** 1. -3 2. -2 3. -1 4. 0 5. 1 6. 2 7. 3 8. 4 To match an interval with its rate of change, compare the corresponding section of the graph and determine whether the function is increasing or decreasing, and by how much. The rate of change is the slope of the function over the given interval.
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