Newton's Method

slider2990

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Jul 3, 2005
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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.
 
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.
newton9tg.gif
 
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?
 
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.
 
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