I need to use Newton's method to solve f(x). Can any one tell me what's wrong of my code and how to improve it.

Answer 1

[Yongjian Feng]

what i s your dx?

Answer 2

[David Hill]

a=1:4;
tiny=1e-10;
x=ones(size(a));%this will not work well for the initial guess
for k=1:length(a)
 f=@(x)tan(x)+a(k)*sin(x)./x;
 fp=@(x)sec(x)^2-a(k)*sin(x)/(x^2)+a(k)*cos(x)/x;
 rat=1;
 while rat>tiny
    dx=f(x(k))/fp(x(k));   
    x(k)=x(k)-dx;
    rat=abs(dx/x(k));
 end
end

If you look at your plot, you will realize that there are lots of crossings. Your initial guess for x must be close to the crossing you want.