The graph shows a parabola opening downward, which means the function $f(x)$ has a local maximum at its vertex.

To solve:

(a) All local maximum values of $f$:

The local maximum occurs at the highest point of the graph. By looking at the graph, the vertex is at $(0, 4)$. Therefore, the local maximum value of $f(x)$ is: $\boxed{4}$

(b) All values at which $f$ has a local maximum:

The x-coordinate of the vertex where the local maximum occurs is $x = 0$. Therefore, the value at which $f$ has a local maximum is: $\boxed{0}$

Would you like more details on how to find local extrema from graphs, or any further questions on this?

Here are five related questions to further explore:

1. How do you find the local minima on a graph?
2. What is the difference between a global maximum and a local maximum?
3. Can a function have more than one local maximum or minimum?
4. How do you determine if a point is a local maximum using derivatives?
5. What role does the second derivative test play in finding local maxima?

Tip: When identifying local maxima or minima from a graph, focus on the turning points where the graph changes direction.