1. **Problem Statement:** Given the graph of the derivative function $f'(x)$ for $-1 \leq x \leq 3$, determine the number of inflection points of the original function $f(x)$. 2. **Key Concept:** Inflection points of $f(x)$ occur where the concavity changes, which corresponds to points where the second derivative $f''(x)$ changes sign. 3. **Relation Between $f'(x)$ and $f''(x)$:** Since $f'(x)$ is the first derivative, $f''(x)$ is the derivative of $f'(x)$. Therefore, inflection points of $f(x)$ correspond to points where $f'(x)$ has local maxima or minima (extrema). 4. **Analyzing the Graph of $f'(x)$:** The graph of $f'(x)$ shows two points where the concavity changes, indicating two extrema (a local maximum and a local minimum) in $f'(x)$ within the interval $-1 \leq x \leq 3$. 5. **Conclusion:** Since $f'(x)$ has two extrema, $f(x)$ has two inflection points. **Final answer:** c) 2 inflection points