Approximations of solution using Newton's Method
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I have to implement the Newton method in Matlab to plot the function,its tangent and the first 4 approximations. I would like to show how the algorithm works, that mean that the tangent of one approximation finds the next approximation. The code I have written is the following:
plot(x,f(x))
hold on
for j=1:4
x_1=x_0-f(x_0)/F(x_0);
tangent=@(x) F(x_0)*(x-x_0)+f(x_0);
line=@(x) (f(x_0)/(x_0-x_1))*(x-x_1);
plot(x_0,f(x_0),x,line(x),x_1,0)
x_0=x_1;
end
where F is the derivative of f and the function f is f(x)=e^x-x/2. Could you tell me if this is right? The plot I got is at the attachment.. Also at the plot the range of y is [-2000,3000], how could I make it smaller so that I can see the approximations better?
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