Repeat Problem 6.20 with an initial guess of \(x(1)=4\).

Data From Problem 6.20:-

Use Newton-Raphson to find one solution to the polynomial equation \(f(x)=y\), where \(y=7\) and \(f(x)=x^{4}+3 x^{3}-15 x^{2}-19 x+30\). Start with \(x(0)=0\) and continue until (6.2.2) is satisfied with \(\varepsilon=0.001\).

Data From Equation 6.2.2:-

- |xx(i+1) xx(i) xx(i) < 8 for all k = 1, 2,..., N , (6.2.2)