How to plot hyperbola curve to pints?

Hello, I have the follwing data given:

x = [0.002 0.01 0.02 0.05 0.12 0.2]

y = [0.2309 3.1405 3.4832 4.0078 4.7561 4.833]

How can I Plot a curved hypobola? I have already tried follwing code but my curve is still edgy and not curved:

hyprb = @(b,x) b(1) + b(2)./(x + b(3));                 % Generalised Hyperbola
NRCF = @(b) norm(y - hyprb(b,x));                       % Residual Norm Cost Function
B0 = [1; 1; 1];
B = fminsearch(NRCF, B0);                               % Estimate Parameters
figure(1)
plot(x, y, 'pg')
hold on
plot(x, hyprb(B,x), '-r')
hold off
grid
text(0.7, 0.52, sprintf('y = %.4f %+.4f/(x %+.4f)', B))

Answer 1

[Daniel Pollard]

You need more values in your vector x. Try it with

x0 = linspace(0.002, 0.2, 100); 

and alter your code to be

hyprb = @(b,x) b(1) + b(2)./(x + b(3));                 % Generalised Hyperbola
NRCF = @(b) norm(y - hyprb(b,x));                       % Residual Norm Cost Function
B0 = [1; 1; 1];
B = fminsearch(NRCF, B0);                               % Estimate Parameters
figure(1)
plot(x, y, 'pg')
hold on
plot(x0, hyprb(B,x0), '-r')
hold off
grid
text(0.7, 0.52, sprintf('y = %.4f %+.4f/(x %+.4f)', B)).

The green points have stayed the same, using your original x and y, but now the red curve has 100 points instead of six, so appears smoother.

[Charnkamal Bhogal]

Thank you very much! Do you know how I can see the formula of the curve?

[Daniel Pollard]

I don't have access to my Matlab machine at the moment, so this is just a stab in the dark but I think if you call

disp(B)

then I think you'll see the three parameters which you named b(1), b(2) and b(3) in the first line.

[Charnkamal Bhogal]

Thank you very much sir!