Answer
absolute minimum value = -1
absolute maximum value = 32
Work Step by Step
Given $f(x)=x^{\frac{5}{3}}$
Critical point occurs where first derivative is zero:
so${\frac{df(x)}{dx}=\frac{x^{\frac{5}{3}}}{dx}}$
${\frac{df(x)}{dx}}=\frac{5}{3}x^{\frac{2}{3}}$
so the critical point is:
$f(0)=0$
test end points:
$f(-1)=(-1)^{\frac{5}{3}}=-1$
$f(8)=8^{\frac{5}{3}}=32$
so absolute minimum value =-1
absolute maximum value =32
