Curve fitting with custom equation, not using toolbox

I have sample X and Y data:

x=[5:5:50];

y=[15 25 32 33 37 35 38 39 41 42];

The data are related by y = a * ( x/(b+x) ) equation

I need to find the coeffs a and b, by curve fitting.

I am trying to use polyfit, but nothing is coming out correctly.

What is the procedure for curve fitting a custom equation? The matalb book I am using is good about basic polynomial equations, and the conversion when converting other equations to polynomials. I am super lost on this one. Thanks.

The answer using Curve fitting toolbox is pasted below, but I can't seem to get there... Help!

General model:

f(x) = (a.*x)/(b+x)

Coefficients (with 95% confidence bounds):

a = 49.58 (45.65, 53.51)

b = 9.943 (7.168, 12.72)

Answer 1

[Stephan]

This example shows how to curve fit with the inbuilt basic function fminsearch , so that no additional toolbox is needed:

https://de.mathworks.com/help/matlab/math/example-curve-fitting-via-optimization.html

[JF]

Thanks, is there any way not using fminsearch? Our book has not covered the fminsearch function, and supposedly this can be solved just using basic commands and polyfit.

The book states: "The curve fitting can be done by writing the reciprocal of the equation and using a first order polynomial." I hope this helps in solving this problem.