From the graph of the function $h$, let’s examine the points where it reaches local minima and the corresponding values.

Observing Local Minima:

1. The graph shows local minima at the points where $h(x)$ has lower values compared to the neighboring points.
2. By inspecting the graph, it appears that the function reaches two local minima at:
   • $x = -2$ where $h(x) \approx -3$
   • $x = 2$ where $h(x) \approx -4$

Answering the Questions:

• (a) All local minimum values of $h$: These are the $y$-values of the local minima.

  • Thus, the local minimum values are $-3$ and $-4$.

• (b) All values at which $h$ has a local minimum: These are the $x$-values where these minima occur.

  • The local minima occur at $x = -2$ and $x = 2$.

Final Answers:

• (a) $-3, -4$
• (b) $-2, 2$

Would you like further details or have any questions?

Here are five additional questions for deeper exploration:

1. What is the difference between local and global minima?
2. How would you find the minima if given the function's formula instead of a graph?
3. What other points (e.g., local maxima) can be identified from this graph?
4. How does one determine the concavity of the function at local minima?
5. How would the answers change if the graph represented a different function type?

Tip: Local minima are points where the function has the lowest values in a small neighborhood but might not be the lowest point overall.