Answer
The absolute maximum $f(0)=0$ and the absolute minimum as $f(-1)=-3, f(1)=-3$.
See graph.
Work Step by Step
Step 1. Given the function $f(x)=-3x^{2/3}, -1\leq x\leq 1$, we have $f(-1)=-3, f(1)=-3$,
Step 2. $f'(x)=-\frac{2}{3}x^{-1/3}$, possible critical point at $x=0$, $f(0)=0$
Step 3. We can identify the absolute maximum as $f(0)=0$ and the absolute minimum as $f(-1)=-3, f(1)=-3$ on the given interval.
Step 4. See graph.