How to find arguments of a given equation in MATLAB

[mohamis288]

I want to know for what values of x, sinc(x) function is going to be half of its max value. Notice that this question can be extended to a more general question such a way that, for example, we can not find inverse of a particular function easily, so we are forced to resort to a simulation software like MATLAB to find the arguments by which equation can be solved. I want to use value of this argument in my future computation in MATLAB. How can I do this in MATLAB?

 

[tepalia02]

I want to know for what values of x, sinc(x) function is going to be half of its max value. Notice that this question can be extended to a more general question such a way that, for example, we can not find inverse of a particular function easily, so we are forced to resort to a simulation software like MATLAB to find the arguments by which equation can be solved. I want to use value of this argument in my future computation in MATLAB. How can I do this in MATLAB?

I think you can get some help from here: https://www.mathworks.com/matlabcentral/answers/1946044-how-to-obtain-argument-value-of-an-equation

 

[albbg]

You could use the built-in "fzero" function to search the zero of a non-linear funcion in a given interval.

For instance, using the proposed question :

sinc(x) = max(sinc(x))/2:

you can do the work using two functions:

clear % Clear all variables
fun=@(x) sinc(x) % Initial function
xm=[0:0.01:10]; % Search interval for maximum
mx=max(fun(xm)); % Find maximum of "fun"
x0=[0 10]; % Search interval for zero
fun1=@(x) fun(x)-mx/2; % Function to which search for zero
[x vl exf otp] = fzero(fun1,x0) % Find the zero of "fun1"

Only one zero must to be contained in the search interval x0.