Answer
$(-1,0)$ and $(1,1)$
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.
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Observing from left to right,
From being negative, slope changes to zero at x=-2 (increases, concave up).
After x=-2, it becomes positive and increases (still concave up)
At x-1 it stops increasing and starts decreasing to 0 (becomes concave down),
decreases to 0 at the local maximum at x=0, after which it becomes negative and continues to decrease (concave down)
At x=1, it stops decreasing and starts changing from negative to zero (increases, concave up),
becomes zero at the minimum at x=1.5, from where it becomes positive, always increasing (concave up).
Change of concavity at $x=-1$ and at $x=1$
Inflection points: $(-1,0)$ and $(1,1)$
