Calculus of a Single Variable, Chapter 3, 3.1, Section 3.1, Problem 24

Given: f(x)=root(3)(x), [-8, 8]
Find the critical values for x by setting the derivative equal to zero and solving for the x value(s).
f(x)=x^(1/3)
f'(x)=(1/3)x^(-2/3)=0
f'(x)=1/(3x^(2/3))=0
1=0
1=0 is not a true statement. Therefore the critical x value(s) does not exist.
Plug in the critical value(s), if one exists, and the endpoints of the interval into f(x).
f(x)=root(3)(x)
f(8)=root(3)(8)=2
f(-8)=root(3)(-8)=-2


Examine the f(x) values to determine the absolute extrema.
The absolute minimum value is the point (-8 -2).
The absolute maximum value is the point (8, 2).