When the graph of $f'(x)$ has a point of inflection, what feature shows in the graph of $f(x)$ at that point?
Similar to how when $f'(x)$ has a root $f(x)$ has a turning point there, and when $f'(x)$ touches the $x$-axis $f(x)$ has a horizontal point of inflection there.
A point of inflection in the graph of $f'(x)$ is the same as a turning point in the graph of $f''(x)$. Since $f''(x)$ represents the concavity of $f(x)$, an inflection point in the graph of $f'(x)$ represents a point in the graph of $f(x)$ where its concavity has a local maximum or minimum.