Answer
(a). $f'(x) = \frac{2}{3}x^{−1/3} $, which is never zero. However,
there is a point in the domain (namely $(0, 0)$) where the derivative doesn’t exist. So this is the only critical point.
(b). We have $f(−8) = 4 = f(8)$, and $f(0) = 0$. So the
absolute maximum of $f$ on this interval is $4$ and
the absolute minimum is $0$.
Work Step by Step
See the graph for explanation.
