Use the graph to determine the following. Q (a) Find the numbers at which f has a relative maximum. What are these relative maxima? (b) Find the numbers at which f has a relative minimum. What are these relative minima? 23456 (a) The number(s) at which f has a relative maximum islare (Type an integer or a decimal. Use a comma to separate answers as needed.)

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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### Analyzing Relative Extrema from a Graph

#### Instructions:
Use the graph provided to determine the following:

1. **(a) Find the numbers at which \( f \) has a relative maximum. What are these relative maxima?**
2. **(b) Find the numbers at which \( f \) has a relative minimum. What are these relative minima?**

#### Description of the Graph:
- The graph is a plot of a function \( f(x) \) with the following features:
  - It is a continuous curve that intersects the y-axis at \( y = 0 \).
  - The graph shows a clear parabolic shape with peaks and valleys.

#### Explanation of Features:
- **Axes**: The graph is plotted with the x-axis ranging from -6 to 6 and the y-axis ranging from -8 to 6.
  - The point of intersection (origin) is marked at (0, 0).
- **Relative Maximum**:
  - The graph has a peak at \( x = -3 \) with a value roughly around \( y = 5 \).
  - This peak is a relative maximum.
- **Relative Minimum**:
  - The graph dips to a trough at \( x = 0 \) with a value of \( y = -6 \).
  - There is another trough at \( x = 3 \) with a value roughly around \( y = 0 \).
  - These troughs are relative minima.
  
#### Questions:
**(a) The number(s) at which \( f \) has a relative maximum is/are \(\_\_\_\_\_\).**
- (Type an integer or a decimal. Use a comma to separate answers as needed.)

**(b) The number(s) at which \( f \) has a relative minimum is/are \(\_\_\_\_\_\).**
- (Type an integer or a decimal. Use a comma to separate answers as needed.)

By examining the provided graph, you can identify the x-coordinates of the relative maxima and minima. Insert the corresponding x-values in the provided answer fields.
Transcribed Image Text:### Analyzing Relative Extrema from a Graph #### Instructions: Use the graph provided to determine the following: 1. **(a) Find the numbers at which \( f \) has a relative maximum. What are these relative maxima?** 2. **(b) Find the numbers at which \( f \) has a relative minimum. What are these relative minima?** #### Description of the Graph: - The graph is a plot of a function \( f(x) \) with the following features: - It is a continuous curve that intersects the y-axis at \( y = 0 \). - The graph shows a clear parabolic shape with peaks and valleys. #### Explanation of Features: - **Axes**: The graph is plotted with the x-axis ranging from -6 to 6 and the y-axis ranging from -8 to 6. - The point of intersection (origin) is marked at (0, 0). - **Relative Maximum**: - The graph has a peak at \( x = -3 \) with a value roughly around \( y = 5 \). - This peak is a relative maximum. - **Relative Minimum**: - The graph dips to a trough at \( x = 0 \) with a value of \( y = -6 \). - There is another trough at \( x = 3 \) with a value roughly around \( y = 0 \). - These troughs are relative minima. #### Questions: **(a) The number(s) at which \( f \) has a relative maximum is/are \(\_\_\_\_\_\).** - (Type an integer or a decimal. Use a comma to separate answers as needed.) **(b) The number(s) at which \( f \) has a relative minimum is/are \(\_\_\_\_\_\).** - (Type an integer or a decimal. Use a comma to separate answers as needed.) By examining the provided graph, you can identify the x-coordinates of the relative maxima and minima. Insert the corresponding x-values in the provided answer fields.
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