Hi,
this answer comes a bit late, but I wish someone still finds this information usefull.
Lipschits constant is defined as
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/624878/image.png)
From the mean value theoream one can see that
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/624883/image.png)
so at every point if the constant Lis greater or equal than the norm of the functions derivative, then L is the Lipschitz constant.
The procedure to find the Lipschitz constant is to calculate the derivative of the function and then check if the derivative function is bounded by some value L on the domain - - that is your Lipschits constant.
Usually the norm is the euclidean-norm ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/624888/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/624888/image.png)
You can do the calculations with symbolic toolbox
syms x
f = sin(x); % here we define the function
df = diff(f) % here we calculate the derivative function of sin(x)
df = abs(df) % here we use the euclidean norm
fplot(df) % plots the abs(df). The function is clearly limited with upper bound M=1
% so the Lipschits constant is L >= 1