Question

solve equation x4-x-9=0 by newtonraphson

Answer 1

set \(f(x)=x^4-x-9\)

\[f'(x)=4x^3-1\]

because \(f(1)=-9\) and \(f(2)=5\), there exists at least one root \(1<x_r<2\).

choose an initial value \(1<x_1<2\) then use the newton's method
\[\Large x_{n+1}=x_n+\frac{f(x_n)}{f'(x_n)}\]