Mathematics

The key is finding where $s'(x) = 0$ or doesn't exist—these are your only candidates for local extrema. You'll need to use the product rule carefully on $x^{2/3}(x-3)$, and remember that $x^{2/3}$ has a derivative that blows up at $x=0$. Once you have all critical points, use the first derivative test (checking the sign of $s'(x)$ on either side) to classify each as a max or min.

The key is finding where $s'(x) = 0$ or doesn't exist—these are your only candidates for local extrema. You'll need to use the product rule carefully on $x^{2/3}(x-3)$, and remember that $x^{2/3}$ has a derivative that blows up at $x=0$. Once you have all critical points, use the first derivative test (checking the sign of $s'(x)$ on either side) to classify each as a max or min.