Newton's Method

[slider2990]

In using Newton's method how do you determine the first approximation value without looking at a graph of the fucntion?

For an example please do: Find the real root approximated to 2 decimal places x^3+5x-3=0

thanks ahead of time for the much needed help.

 

[pka]

If f(x)= x<SUP>3</SUP>+5x-3 then f(0)<0 and f(1)>0.
So there is a root between 0 and 1. So you could use 0.5 as the first approximation.

 

[slider2990]

so just use the intermediate value theorem to find the interval in which to select the first approximation? or are the other methods still excluding graphing?

 

[tkhunny]

Wild guess?

Empirical Observation?

With ONLY one solution, life is simpler, and there is not much concern. Just pick a value and hope for the best.

With multiple solutions, you enter a different world. It is a very interesting and complex study, determining which starting values converge to which solutions.