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Consider the graph of f'(x), shown in blue below. Submit your answer to this question by completing the following tasks: 1. How many local maxima does f(x) have? Use the slider on the lower left corner of the graph to select the number of local maxima of f(x). 2. Identify the x-coordinate of each local maximum of f(x) by dragging the corresponding movable dot to a point on the graph of f'(x). Provide your answer below:

Consider the graph of f'(x), shown in blue below. Submit your answer to this question by completing the following tasks: 1. How many local maxima does f(x) have? Use the slider on the lower left corner of the graph to select the number of local maxima of f(x). 2. Identify the x-coordinate of each local maximum of f(x) by dragging the corresponding movable dot to a point on the graph of f'(x). Provide your answer 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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### Identifying Local Maxima of a Function Using Its Derivative Graph Consider the graph of \( f'(x) \), shown in blue below. Submit your answer to this question by completing the following tasks: 1. **Determine the Number of Local Maxima of \( f(x) \):** - Use the slider on the lower left corner of the graph to select the number of local maxima of \( f(x) \). 2. **Identify the x-coordinate of Each Local Maximum:** - Drag the corresponding movable dot to a point on the graph of \( f'(x) \). ### Graph Description and Interaction Below the instructions, there is a dynamic graph of the derivative \( f'(x) \). The x-axis ranges from -8 to 8, and the y-axis ranges from -8 to 8. The blue curve represents the derivative \( f'(x) \) of the function \( f(x) \). #### Detailed Description of the Graph: - The curve \( f'(x) \) passes through multiple turning points and inflection points. - The significant features are: - A local minimum at \( x \approx -1.5 \) - A local maximum at \( x \approx 1 \) - A steep local minimum at \( x \approx 3 \) - A rise towards high y-values as \( x \rightarrow 4 \) #### Interaction Tools: - **Number of Local Maxima Slider:** - Located at the bottom left corner, this slider allows users to select the number of local maxima detected in \( f(x) \). The options range from 0 to 3. ### Instructions to Users 1. **Determine the Number of Local Maxima:** - Assess the graph of \( f'(x) \) for points where the slope changes from positive to negative as these indicate local maxima of \( f(x) \). 2. **Drag and Drop the Movable Dots:** - Identify the x-coordinates where the derivative \( f'(x) \) changes from positive to negative. Move the dots to these points to mark the local maxima of \( f(x) \). Provide your answers and adjustments below this graph interface. Use the interactive features to effectively highlight and communicate your findings of local maxima for \( f(x) \). **Note:** If required, you can reset the settings and begin again by clicking on the "RESET"
Transcribed Image Text:### Identifying Local Maxima of a Function Using Its Derivative Graph Consider the graph of \( f'(x) \), shown in blue below. Submit your answer to this question by completing the following tasks: 1. **Determine the Number of Local Maxima of \( f(x) \):** - Use the slider on the lower left corner of the graph to select the number of local maxima of \( f(x) \). 2. **Identify the x-coordinate of Each Local Maximum:** - Drag the corresponding movable dot to a point on the graph of \( f'(x) \). ### Graph Description and Interaction Below the instructions, there is a dynamic graph of the derivative \( f'(x) \). The x-axis ranges from -8 to 8, and the y-axis ranges from -8 to 8. The blue curve represents the derivative \( f'(x) \) of the function \( f(x) \). #### Detailed Description of the Graph: - The curve \( f'(x) \) passes through multiple turning points and inflection points. - The significant features are: - A local minimum at \( x \approx -1.5 \) - A local maximum at \( x \approx 1 \) - A steep local minimum at \( x \approx 3 \) - A rise towards high y-values as \( x \rightarrow 4 \) #### Interaction Tools: - **Number of Local Maxima Slider:** - Located at the bottom left corner, this slider allows users to select the number of local maxima detected in \( f(x) \). The options range from 0 to 3. ### Instructions to Users 1. **Determine the Number of Local Maxima:** - Assess the graph of \( f'(x) \) for points where the slope changes from positive to negative as these indicate local maxima of \( f(x) \). 2. **Drag and Drop the Movable Dots:** - Identify the x-coordinates where the derivative \( f'(x) \) changes from positive to negative. Move the dots to these points to mark the local maxima of \( f(x) \). Provide your answers and adjustments below this graph interface. Use the interactive features to effectively highlight and communicate your findings of local maxima for \( f(x) \). **Note:** If required, you can reset the settings and begin again by clicking on the "RESET"
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