Answer
$(-1,-1)$ 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,
The slope changes from negative to zero (increases, concave up) at the local minimum at x=-1.5,
where where it becomes positive and increases (still concave up) up to x=-1.
At x=-1 it stops increasing and starts decreasing (becomes concave down),
decreases to zero at the local maximum at x=0,
after which it becomes negative and decreases further (still concave down)
until x=1, from where it starts rising from negative to zero (becomes concave up),
becomes zero at the local minimum at x=1.5, after which it becomes positive,
and continues to increase (remains concave up)
Change of concavity at $x=-1$ and at $x=1$
Inflection points: $(-1,-1)$ and $(1,-1)$
