How to determine where the function is equal 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)

Answer 1

[Matt J]

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]

[Lauren Stearns]

It worked! Thank you so very much for your help! :D

Answer 2

[Ahmed Hossam]

Try to use symbolic calculation to find 'the zeros'. Otherwise use numerical newton raphson algorithm.