To determine the local minimum of the function using the provided graph, we need to identify the point where the function reaches its lowest value in a specific region of the graph.

Looking at the graph:

1. The graph appears to have a local minimum where the curve dips the lowest before increasing again.
2. The point where this happens is around $x = 2$ on the x-axis.
3. At $x = 2$, the graph reaches a value of approximately -2 on the y-axis.

Therefore, the local minimum of the function is -2.

Would you like more details or have any questions?

Here are some related questions that might help further your understanding:

1. What is the difference between a local minimum and a global minimum?
2. How can we find local minima using calculus (derivatives)?
3. What is the significance of concavity in determining local minima and maxima?
4. How do you determine if a function has multiple local minima?
5. What are some examples of real-world applications where finding a local minimum is useful?

Tip: When analyzing graphs, always look for the points where the curve changes direction to identify local maxima and minima.