Please help me to solve this newton-raphson method

How can I use Newton-Raphson method to determine a root of

f (x) = x5−16.05x4+88.75x3−192.0375x2+116.35x +31.6875

using an initial guess of x = 0.5825 and εs = 0.01%.

[James Tursa]

What have you done so far? Have you written any code yet?

[Luis Varela]

On Newton Raphson method, you need calculate the function f(x) and the derivate f'(x), to get the next value of x, and continue while the error is greater than desired, for example:

x = 0.5825;

e=1;

while e>0.01

fx= x^5 - 16.05*x^4 + 88.75*x^3 - 192.0375*x^2 + 116.35*x + 31.6875;

dfx= 5*x^4 - 4*16.05*x^3 + 3*88.75*x^2 - 2*192.0375*x + 116.35;

x2=x-(fx/dfx);

e=100*abs((x2-x)/x2);

x=x2;

end

At the end x will have the value of the calculated root, aprox. x=6.5

Answer 1

[Jakub Rysanek]

In this case I would go with

roots([1,-16.05,88.75,192.0375,116.35,31.6875])

Answer 2

[Luis Varela]

On Newton Raphson method, you need calculate the function f(x) and the derivate f'(x), to get the next value of x, and continue while the error is greater than desired, for example:

x = 0.5825;

e=1;

while e>0.01

fx= x^5 - 16.05*x^4 + 88.75*x^3 - 192.0375*x^2 + 116.35*x + 31.6875;

dfx= 5*x^4 - 4*16.05*x^3 + 3*88.75*x^2 - 2*192.0375*x + 116.35;

x2=x-(fx/dfx);

e=100*abs((x2-x)/x2);

x=x2;

end

At the end x will have the value of the calculated root, aprox. x=6.5