It looks like the image represents a function $f(x)$ plotted on a coordinate plane, showing various points $x_0, x_1, x_2, x_3, x_4, x_5$ on the x-axis, with their corresponding points on the function marked.

Given that no specific task or question is explicitly mentioned, I will infer that you're likely asking which points are local minima or maxima, points of inflection, or zeros based on the graph. Let’s analyze each point.

• $x_0$: Appears to be a zero crossing, as the function intersects the x-axis.
• $x_1$: A zero of the function since $f(x_1) = 0$.
• $x_2$: Appears to be a local maximum as the function peaks here.
• $x_3$: Appears to be a local minimum as the function dips here.
• $x_4$: Another local maximum.
• $x_5$: A local minimum.

Selection based on the graph:

• If you're asked to select all local maxima: Choose $x_2$ and $x_4$.
• If you're asked to select all local minima: Choose $x_3$ and $x_5$.
• If you're asked for zeros: Choose $x_0$ and $x_1$.

Feel free to clarify the specific request! Would you like more details or have any questions about this?

Here are some relative questions to further explore:

1. What are the conditions for a function to have a local minimum or maximum?
2. How can the first derivative test be applied to identify these critical points?
3. What is the difference between a local minimum and a global minimum?
4. How do you determine points of inflection from a graph?
5. How does concavity relate to the second derivative?

Tip: To determine whether a critical point is a minimum or maximum, the second derivative test is useful. If $f''(x) > 0$, the function is concave up, indicating a minimum, while $f''(x) < 0$ implies a maximum.