Answer
Points of inflection of $f$ at $x=-2$ and $x=-1$.
Work Step by Step
A curve is concave up if its slope is increasing, in which case the second derivative is positive.
A curve is concave down if its slope is decreasing, in which case the second derivative is negative.
A point in the domain of $f$ where the graph of $f$ changes concavity, from concave up to concave down or vice versa, is called a point of inflection.
At a point of inflection, the second derivative is either zero or undefined.
The graph of $f'$ is the graph of slope of $f.$
At local (internal) extrema of $f',$ the second derivative is 0.
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At $x=-2,\ f'$ has a relative maximum ($f''$ is undefined because of the spike)
At $x=-1,\ f'$ has a relative minimum
At $x=-1,\ f'$ has a stationary point, but it's neither a minimum nor maximum - no inflection for f.
Points of inflection of $f$ at $x=-2$ and $x=-1$.
