Question

what is the relative extrema of the function x^(2/3)-3 ?

Answer 1

Take the derivative to get:
\[\psi(x)=x^{2/3}-3 \implies \psi'(x)=(2/3)x^{-1/3}\]
We can see by inspection that the derivative can never be zero therefore there are no extrema.
Verification:
http://www.wolframalpha.com/input/?i=plot+y%3Dx%5E(2%2F3)-3

It does have a vertical tangent line at x=0 however, but this is a point of inflection.