# Approximate a value using Newton's method

I'm trying to find an approximation for $11^{\frac{1}{3}}$ by using Newton's method using $x_0 = \frac{3}{2}$. Now my problem only tells me to use a "suitable" function and that threw me off quite a bit. I know this is kind of a weak question, but could anyone explain/give me a hint how I can find a suitable function?

• Newton's method finds roots, so to use it you need some function which has $11^{1\over 3}$ as a root. But you also need one that evaluting doesn't require you to already know $11^{1\over 3}$. littleO's answer gives the obvious choice. – Paul Sinclair Oct 22 '15 at 22:06

You want to find a root of the polynomial $f(x) = x^3 - 11$.