Answer
$(1, 0)$
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 is positive and decreases until the local maximum at x=1, (concave down),
becomes negative and continues to decrease to the x-intercept at x=1, (still concave down),
and after x=1, the slope becomes less negative, increases (concave up),
reaches 0 at the local minimum at x=2 (still concave up),
from where it (the slope) continues increasing (concave up) .
Inflection point at $(1, 0)$
(f changes from concave down to concave up.)
