MATLAB: How to determine where the function is equal to zero

function = to zero

Ultimately I need to figure out the first time my function is equal to zero, but to start I just want to save the x value as a new variable whenever y = 0. Here is my code so far:
    close all; clear all; clc
    % Prepared by Lauren Stearns
    x= 0:10;   
    x(1)= 1E-5;   
    f= @(x) (2*besselj(1,x)./x).^2;    % The Given Function
    y=f(x)                             % replace the first element in the array
    plot(x,y,'b-');                    % Plot the Airy pattern
    hold on;
    xq=0:10;                           % Points of inquiry
    xq(1)=0.0001;
    yq3 = interp1(x,y,xq,'cubic');     % Cubic Interpolation
    plot(xq,yq3,'b.');                 % Plotting the Cubic Interpolation
    for y = 0                          % Trying to save the x value as a new variable 
    when y = 0
        x = Dark_Fringe
    end
    xlabel('x');
    ylabel('f(x)');
    title('Airy Pattern Three');
    disp(Dark_Fringe)

Best Answer

Ultimately I need to figure out the first time my function is equal to zero,
This is the simpler of the two problems. It is equivalent to finding where the bessel function is equal to zero. Using online tables or your plots, you can see that the first root lies in the interval [3.5,4.5]
    >> [xroot,fval] = fzero(@(x) besselj(1,x),  [3.5,4.5])
    xroot =
        3.8317
    fval =
       7.2971e-17
You can do similarly for the other roots in the interval [0,10]
Related Question