From the provided image, we need to determine the relative minimum and maximum points based on the graph.

Let's break down each part of the question:

(a) For what value(s) of $x$ does the function obtain a relative minimum?

Observing the graph, it appears that there is a minimum point at $x = -1$ where the graph dips down to the lowest local value in that vicinity. So:

• Answer: The function has a relative minimum at $x = -1$.

(b) Find the relative minimum value.

The relative minimum value corresponds to the $y$-value at $x = -1$. According to the graph, the point at $x = -1$ has $y = -9$.

• Answer: The relative minimum value is $-9$.

(c) For what value(s) of $x$ does the function obtain a relative maximum?

Looking at the graph, a relative maximum appears to occur at $x = -7$, where the function reaches a peak locally.

• Answer: The function has a relative maximum at $x = -7$.

(d) Find the relative maximum value.

The relative maximum value corresponds to the $y$-value at $x = -7$. From the graph, this point appears to have $y = 7$.

• Answer: The relative maximum value is $7$.

If you'd like more details or have any questions about this solution, feel free to ask!

Here are some related questions to explore:

1. How do we determine relative minima and maxima from the derivative of a function?
2. What is the difference between absolute and relative extrema?
3. Can a function have more than one relative minimum or maximum?
4. What role does the second derivative play in identifying minima and maxima?
5. How can we estimate values from a graph if we don't have precise coordinates?

Tip: When analyzing a graph, look for points where the slope changes from positive to negative (for maximum) or from negative to positive (for minimum).