Answer
No inflection points (concave down everywhere).
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 being very steep (positive) to zero (decreases, concave down)
at the local maximum point at x=1.
From x=1 rightwards, the slope becomes more and more negative (decreases, still concave down)
No change in concavity.
No inflection points (concave down everywhere).
