Approximations of solution using Newton's Method

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?

[Walter Roberson]

What is the point of constructing "tangent" there? Remember it is going to be overwritten in the next iteration of the "for" loop.

It is not recommended to name a variable "line" as line() is the name of the command to draw lines in MATLAB.

[evi]

Ok, I changed the name of the variable... I wanted to check firstly if the graph of the function and the approximations are plotted right... Are they right?? As you can see the y-axis is from -2000 to 3000, how can I change that so that I can see the resuts better???

[Walter Roberson]

See xlim and ylim

[evi]

At the beginning of the function I wrote

x=-2:0.00001:8;
ylim([-4 6])

but there is no change...Why? Do I something wrong??

[Walter Roberson]

Set ylim after you plot.

[evi]

Great now it shows only a specific range of y!! Could you also tell me how the x-axis & y-axis could be shown in the plot??