Answer
Inflection points of $f(x)$ at $ x=0$ and $x=1.$
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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Points where $f''$ crosses the axis (changes signs): $\quad$
at $x=0.$
Points where its graph is broken:
positive on one side of the break and negative on the other:$\quad x=1$
Inflection point of $f(x)$ at $ x=0$ and $x=1.$
