Chapter 4.1, Problem 25ES

Find: (a) the intervals on which $f$ is increasing, (b) the intervals on which $f$ is decreasing, (c) the open intervals on which $f$ is concave up, (d) the open intervals on which $f$ is concave down, and (e) the x-coordinates of all inflection points.

$f\left(x\right)={\left(x^{2/3}-1\right)}^2$