Originally Posted by

**jvignacio** hi guys, just a question on newtons method. I want to know how to do determine the first value we input into the equation? So for Xo ? i know you could guess this and just start the iterations from there but might take longer than knowing an initial value to start with so its shorter and you get more accurate results

for example

$\displaystyle x^3 = 4x + 1$

$\displaystyle x^3 - 4x - 1 = 0$

$\displaystyle f(x) = x^3 - 4x - 1$

$\displaystyle f ' (x) = 3x^2 - 4$

then we have $\displaystyle x - \frac {f(x)}{f'(x)}$

Xo = ?

$\displaystyle X1 = Xo - \frac {(Xo)^3 - 4(Xo) - 1}{3(Xo)^2 - 4}$

so Xo would start with? thanks for the help.