To identify the inflection points of $f$, we need to analyze the graph of its derivative, $f'$. Inflection points of $f$ occur where $f'$ changes from increasing to decreasing or vice versa, which corresponds to the critical points of $f'$ (local minima or maxima) on the graph.

Looking at the graph, we can observe the following:

1. At $x = -2$, there is a local minimum.
2. At $x = -1.0$, there is a local maximum.
3. At $x = -0.3$, there is another local minimum.

These points indicate changes in concavity for $f$, meaning they are potential inflection points.

Thus, the correct selections would be:

• $x = -2$
• $x = -1.0$
• $x = -0.3$

Would you like a deeper explanation or have any further questions on this?

Here are some related questions to expand on this concept:

1. What are the conditions for a function to have an inflection point?
2. How can we identify inflection points by analyzing the second derivative $f''$?
3. Why do the critical points of $f'$ indicate changes in concavity of $f$?
4. What would the graph of $f$ look like given this $f'$ graph?
5. How would inflection points change if $f'$ had additional critical points?

Tip: Remember, inflection points of a function $f$ occur where the second derivative $f''$ changes sign. This is often indicated by local extrema in $f'$, as shown here.