To determine the local maximum of the graph, we need to identify the highest point on the curve in a particular region (before it starts to decrease again).

Looking at the graph you've provided, it appears to be a polynomial function with a clear local maximum around $x = -2$. At this point, the curve reaches its highest value before decreasing.

The exact value of the local maximum would depend on the specific function represented by the graph. However, based on the visual inspection, it seems that the local maximum occurs around $x = -2$, where the value of $y$ is approximately 1.

If you have the equation of the function, I could provide a more precise calculation.

Do you have any other questions or need further details?

Here are five related questions:

1. Do you want to determine the local minimum on this graph as well?
2. Are you interested in finding the derivative to confirm the critical points?
3. Would you like help identifying other key features of the graph, such as inflection points?
4. Are you trying to determine the global maximum or minimum?
5. Do you need assistance with the function’s behavior as $x$ approaches infinity or negative infinity?

Tip: To find the exact local maximum of a function, you can take its derivative, set it equal to zero, and solve for $x$. Then, use the second derivative to confirm whether it's a maximum.