Notice above that the values of f(t) and f'(t) are much more complex in nature than the example (f(t)=4*t-8 with f'(t)=4) I gave you on the previous page to illustrate Newton-Raphson. Because the prediction equation is so much more complex, it took more iterations to solve for the true value of t.
Try substituing other guesses and see how many iterations it takes to hit the same predicted "drop dead" time performance. You can even guess ridiculously with 1 minute or as much as 366 minutes and it will still kick out the correct answer. It goes to show that guy Newton was pretty smart--his math not only computes your best performance time, but he is also the guy who came up with the equations of how hard and how fast you hit the pavement when you trip over the finish line!
A word of caution: As I mentioned earlier, oxygen uptake alone is not a good predicter of race performance capability because there are other factors such as how soon a runner will hit his or her lactate turnpoint that mitigate its effective influence on performance either positively or negatively. Daniels and Gilbert, with their "drop dead" equation forced every runner into the same running economy category as that of an elite athlete. Few people have that type of profile in reality.