Deriving functions relating to condition numbers

[mabelw]

I have a question stating to derive the functions x |-> f_1(x)=x^3 and f_2(x)=thirdrootof(x) on their domains of definition based on the asymptotic relative condition number KR = KR(f,x). I'm not sure where to start with this question, I'm not sure if I even understand it. Do I find the condition number for each of the functions?

 

[Mark44]

I moved your post from the Homework section you started it in. Be advised that homework questions must use the homework template that you deleted.

Your functions are $f_1(x) = x^3$ and $f_2(x) = \sqrt[3]{x}$. Rightclick on either of the expressions I wrote to see the LaTeX script I used.
This wiki article discusses condition numbers -- https://en.wikipedia.org/wiki/Condition_number -- see the section titled "One variable." The condition number for a nonlinear function is $\frac {x f'(x)}{f(x)}$, so you will need to differentiate your two functions, not derive them.