https://file.aiquickdraw.com/mathbot/file/1727473231824y0zd0brx.jpg

Let's go through the questions one by one using the graph provided:

### a. For what value(s) of x does the function obtain a relative minimum?
- A **relative minimum** occurs at the lowest point in a certain interval.
- On the graph, the lowest points appear to be at **(-17, -51)** and **(-10, -100)**.
- Hence, the x-values where the relative minima occur are **x = -17** and **x = -10**.

Answer: **x = -17 and x = -10**

### b. Find the relative minimum value.
- The **relative minimum values** correspond to the y-values of the points where the function has a relative minimum.
- From the graph, the relative minima occur at **(-17, -51)** and **(-10, -100)**.
- The **relative minimum values** are **-51** and **-100**.

Answer: **The relative minimum values are -51 and -100**

### c. For what value(s) of x does the function obtain a relative maximum?
- A **relative maximum** occurs at the highest point in a certain interval.
- On the graph, the highest points appear to be at **(10, 100)** and **(18, 36)**.
- Hence, the x-values where the relative maxima occur are **x = 10** and **x = 18**.

Answer: **x = 10 and x = 18**

### d. Find the relative maximum value.
- The **relative maximum values** correspond to the y-values of the points where the function has a relative maximum.
- From the graph, the relative maxima occur at **(10, 100)** and **(18, 36)**.
- The **relative maximum values** are **100** and **36**.

Answer: **The relative maximum values are 100 and 36**

Would you like more details or clarifications on any part? Here are some related questions to expand your understanding:

1. How do you distinguish between absolute and relative extrema on a graph?
2. What is the significance of critical points in finding relative maxima or minima?
3. How do second derivatives help in determining whether a point is a maximum or minimum?
4. Can a function have more than two relative extrema?
5. How do you find relative extrema algebraically using derivatives?

**Tip:** When analyzing graphs, always pay attention to the turning points for finding relative extrema, as they indicate potential maximum or minimum values.

Use the graph below to answer the following questions: 

a. For what value(s) of x does the function obtain a relative minimum? 
b. Find the relative minimum value. 
c. For what value(s) of x does the function obtain a relative maximum? 
d. Find the relative maximum value.

Learn how to identify the relative maximum and minimum values from a given graph. This example covers finding x-values and y-values for relative extrema, analyzing turning points, and understanding graph behavior. Suitable for high school students in Grades 10-12.

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