Answer
Absolute minimum is $-1$ at $x=-1,$
absolute maximum is $32$ at $x=8$
Work Step by Step
To find absolute extrema of a continuous function f on a closed interval:
1. Evaluate $f$ at all critical points and endpoints.
2. Take the largest and smallest of these values.
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f is continuous on $[-1,8]$.
Critical points:
$f'(x)=0$
$\displaystyle \frac{5}{3}x^{2/3}=0$
$x=0 , \quad f(0)=0.$
Endpoints:
$f(-1)=[(-1)^{5}]^{1/3}=(-1)^{1/3}=-1,$
$f(8)=(8^{1/3})^{5}=2^{5}=32$
