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.