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# Newton Raphson's-method

Posts: 2Member
I need to find the two positive roots of f(x) = 60x -(x^2+x+0.1)^6/(x+1)^6 -10x*exp(-x)= 0 with Newton Raphson's method. What I've done is this:

format long

xa = [-0.5: 0.01: 0.5];
xA = [1.5: 0.01: 3];

f = @(x) 60*x - ((x.^2+x+0.1).^6)./((x+1).^6) - 10*x.*exp(-x);

fprim = @(x) (6*((x.^2+x+0.1).^5)*(x.^2+2*x+0.9))/((x+1).^7);

[color=Red]%fprim = @(f,x) diff(f([x])) - I would like to do something like this instead, but it doesn't work for me.[/color]
figure(1)
subplot(211)
plot(xa, f(xa))

subplot(212)
plot(xA, f(xA))

% startvalues x = 0, x= 2

xstart = [0 2];
for i = 1: length(xstart)
x = xstart(i);
dx = 1;
iter = 0;
f(x);
fprim(x);
disp('x dx')
disp('-----------------------------')
while abs(dx/x) > 1e-6 && iter<100
dx = -f(x)/fprim(x);
x = x + dx;
iter = iter+1;
disp([x abs(dx)]);
end
disp(['____________'])
end

Can anyone see what I did wrong? I guess there is something wrong with my [b]fprim[/b] and that's why I would like to calc this in MATLAB.

As you see I estimate my y=0 to x=0 and x=2. Did I do anything wrong here?

Help is highly appreciated,
R