Answer
$(1,1)$
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,
$(-\infty,0)\quad$ slope decreases (concave down) from very steep (positive),
to zero at the local maximum at x=-1,
from where it continues to decrease (becomes steeper with negative slope).
No changes in concavity on this interval. Concave down.
$(0,+\infty)\quad$ The slope changes from very negative to less negative (increases: concave up)
until x=1, from where the change is to become more negative (decreases, concave down)
Change of concavity at $x=1$.
Inflection point: $(1,1)$
