I'm doing a MATLAB assignment in which you work out and implement a better version of Newton-Raphson using a second degree Taylor polynomial instead of a first degree one. I have the algorithm worked out and it is working good. The second part of the assignment is to study the order of convergence empirically. The problem is that with all the functions I've come up with so far gets a very good answer after only 2-4 iterations which doesn't give me a very reliable grounds for analyzing the order of convergence.
Can you help me come up with a function that the N-R method works on pretty badly, so that it, for some starting value, takes some more iterations to get to a good value?